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Using matrix product state techniques we study the nonequilibrium dynamical response of the half-filled Hubbard ladder when subject to an optical pump. Optical pumping offers a way of producing and manipulating new strongly correlated phenomena by suppressing existing magnetic correlations. The ladder allows the effects of pump directionality to be investigated, and compared to a single chain it has strong spin-charge coupling and a fully gapped excitation spectrum, promising different nonequilibrium physics. We compute time-dependent correlations, including the nonequilibrium dynamical structure factors for spin and charge. By deriving a combined spin-charge sum rule that applies both in and out-of-equilibrium, we show that spectral weight is pumped directly from the antiferromagnetic spin response into a low energy $\omega\sim 0$ charge response below the Mott gap. The transfer of weight is pump direction dependent: pumping directed along the legs disrupts magnetic correlations more than pumping in the rung direction, even if the post pump energy density is similar. The charge correlation length is dramatically enhanced by the pump, whilst the spin correlations are most strongly suppressed at nearest and next-nearest neighbour spacings. After the pump the system is in a nonthermal correlated metallic state, with gapless charge excitations and approximately equal spin and charge correlation lengths, emphasising the importance of treating these degrees of freedom on an equal footing in nonequilibrium systems., Comment: 18 pages, 18 figures

Quantum computers can efficiently solve problems which are widely believed to lie beyond the reach of classical computers. In the near-term, hybrid quantum-classical algorithms, which efficiently embed quantum hardware in classical frameworks, are crucial in bridging the vast divide in the performance of the purely-quantum algorithms and their classical counterparts. Here, a hybrid quantum-classical algorithm is presented for the computation of non-perturbative characteristics of quantum field theories. The presented algorithm relies on a universal parametrized quantum circuit ansatz based on Euler and Cartan's decompositions of single and two-qubit operators. It is benchmarked by computing the energy spectra of lattice realizations of quantum field theories with both short and long range interactions. Low depth circuits are provided for false vacua as well as highly excited states corresponding to mesonic and baryonic excitations occurring in the analyzed models. The described algorithm opens a hitherto-unexplored avenue for the investigation of mass-ratios, scattering amplitudes and false-vacuum decays in quantum field theories., Comment: 7 pages, 3 figures

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a different approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as $\widetilde{O}(\lambda N^7 |\Omega|^3/(M^{5/2} \epsilon^{3/2})$ where $\lambda$ is the coupling strength, $N$ is the occupation cutoff $|\Omega|$ is the volume of the spatial lattice, $M$ is the mass of the particles and $\epsilon$ is the uncertainty in the energy calculation used for the $S$-matrix determination. Qubitization in the field basis scales as $\widetilde{O}(|\Omega|^2 (k^2 \Lambda +kM^2)/\epsilon)$ where $k$ is the cutoff in the field and $\Lambda$ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of $4\times 10^6$ physical qubits and $10^{12}$ $T$-gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns, placing simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results., Comment: main text, 50 pages, supplementary 64 pages

Conventional wisdom dictates that quantum effects become unimportant at high temperatures. In magnets, when the thermal energy exceeds interactions between atomic magnetic moments, the moments are usually uncorrelated, and classical paramagnetic behavior is observed. This thermal decoherence of quantum spin behaviors is a major hindrance to quantum information applications of spin systems. Remarkably, our neutron scattering experiments on Yb chains in an insulating perovskite crystal defy these conventional expectations. We find a sharply defined spectrum of spinons, fractional quantum excitations of spin-1/2 chains, to persist to temperatures much higher than the scale of the interactions between Yb magnetic moments. The observed sharpness of the spinon continuum's dispersive upper boundary indicates a spinon mean free path exceeding $\approx 35$ inter-atomic spacings at temperatures more than an order of magnitude above the interaction energy scale. We thus discover an important and highly unique quantum behavior, which expands the realm of quantumness to high temperatures where entropy-governed classical behaviors were previously believed to dominate. Our results have profound implications for spin systems in quantum information applications operating at finite temperatures and motivate new developments in quantum metrology., Comment: 17 pages, 4 figures main text plus 19 pages, 7 figures supplementary text

Breast cancer (BC) stands as one of the most common malignancies affecting women worldwide, necessitating advancements in diagnostic methodologies for better clinical outcomes. This article provides a comprehensive exploration of the application of Explainable Artificial Intelligence (XAI) techniques in the detection and diagnosis of breast cancer. As Artificial Intelligence (AI) technologies continue to permeate the healthcare sector, particularly in oncology, the need for transparent and interpretable models becomes imperative to enhance clinical decision-making and patient care. This review discusses the integration of various XAI approaches, such as SHAP, LIME, Grad-CAM, and others, with machine learning and deep learning models utilized in breast cancer detection and classification. By investigating the modalities of breast cancer datasets, including mammograms, ultrasounds and their processing with AI, the paper highlights how XAI can lead to more accurate diagnoses and personalized treatment plans. It also examines the challenges in implementing these techniques and the importance of developing standardized metrics for evaluating XAI's effectiveness in clinical settings. Through detailed analysis and discussion, this article aims to highlight the potential of XAI in bridging the gap between complex AI models and practical healthcare applications, thereby fostering trust and understanding among medical professionals and improving patient outcomes.

Although entanglement is both a central ingredient in our understanding of quantum many-body systems and an essential resource for quantum technologies, we only have a limited ability to quantify entanglement in real quantum materials. Thus far, entanglement metrology in quantum materials has been limited to measurements involving Hermitian operators, such as the detection of spin entanglement using inelastic neutron scattering. Here, we devise a method to extract the quantum Fisher information (QFI) from non-Hermitian operators and formulate an entanglement witness for resonant inelastic x-ray scattering (RIXS). Our approach is then applied to the model iridate dimer system Ba$_3$CeIr$_2$O$_9$ and used to directly test for entanglement of the electronic orbitals between neighboring Ir sites. We find that entanglement is challenging to detect under standard conditions, but that it could be achieved by analyzing the outgoing x-ray polarization or via specific choices of momentum and energy. Our protocol provides a new handle for entanglement detection, which offers routes to related types of entanglement witness (such as orbitally-resolved measurements) and to the generalization to out-of-equilibrium settings accessed in ultrafast settings., Comment: 10 pages, 8 figures

In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems., Comment: 16 pages, 17 figures

A novel cold neutron source (CNS) employing chessboard or staircase assemblies of high-aspect ratio rectangular (HARR) para-hydrogen (p-H2) moderators is proposed. It is demonstrated that this design can generate neutron beams with higher intensity and brightness, up to 2.5 times more than any p-H2 based CNS with an equal cold neutron beam cross-section made of a single moderator (flat or voluminous). Two limiting factors for this gain are identified: the limited volume of the high-density thermal neutron region surrounding the reactor core or spallation target imposing constraints on the total length of the moderator assembly and the finite width of moderator walls. Additional factors affecting gain can be revealed by dedicated Monte Carlo simulations of the moderator-reflector assembly, which can only be conducted for a particular neutron source and are beyond the scope of this general study. Moreover, the relatively large length of moderator assemblies makes their application for short pulse neutron sources very problematic. Analytic approach for calculating the brightness of p-H2 moderators is introduced. Because brightness gain originates from a near-the-surface effect resulting from the prevailing single collision process, HARR CMs offer a significant increase, up to a factor of 10, in cold neutron brightness. The obtained results are in excellent agreement with MCNP calculations. The concept of 'low-dimensionality' (low-d) in moderators is explored: achieving a substantial increase in brightness necessitates CMs to be low-d both geometrically (HARR) and physically, requiring the moderator's smallest dimension to be smaller than the mean free path for thermal neutrons. This explains why additional compression of the CM along the longest direction, effectively giving it a tube-like shape, does not leads to a significant brightness increase comparable to the flattening of CM.

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm~(SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state, but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit-depth that depends not on the system-size, but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system-size were sufficient to generate states with fidelity in excess of 99\%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of non-equilibrium phenomena in quantum simulators., Comment: 11 pages, 6 figures

We present a protocol for detecting multipartite entanglement in itinerant many-body electronic systems using single particle Green's functions. To achieve this, we first establish a connection between the quantum Fisher information (QFI) and single particle Green's functions by constructing a set of witness operators built out of single electron creation and destruction operators in a doubled system. This set of witness operators is indexed by a momenta $k$. We compute the QFI for these witness operators and show that for thermal ensembles it can be expressed as an auto-convolution of the single particle spectral function. We then apply our framework to a one-dimensional fermionic system to showcase its effectiveness in detecting entanglement in itinerant electron models. We observe that the detected entanglement level is sensitive to the wave vector associated with witness operator. Our protocol will permit detecting entanglement in many-body systems using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, two spectroscopies that measure the single particle Green's function. It offers the prospect of the experimental detection of entanglement through spectroscopies beyond the established route of measuring the dynamical spin response., Comment: 6 pages, 3 figures

We propose herein an extension of truncated spectrum methodologies (TSMs), a non-perturbative numerical approach able to elucidate the low energy properties of quantum field theories. TSMs, in their various flavors, involve a division of a computational Hilbert space, $\mathcal{H}$, into two parts, one part, $\mathcal{H}_1$ that is `kept' for the numerical computations, and one part, $\mathcal{H}_2$, that is discarded or `truncated'. Even though $\mathcal{H}_2$ is discarded, TSMs will often try to incorporate the effects of $\mathcal{H}_2$ in some effective way. In these terms, we propose to keep the dimension of $\mathcal{H}_1$ small. We pair this choice of $\mathcal{H}_1$ with a Krylov subspace iterative approach able to take into account the effects of $\mathcal{H}_2$. This iterative approach can be taken to arbitrarily high order and so offers the ability to compute quantities to arbitrary precision. In many cases it also offers the advantage of not needing an explicit UV cutoff. To compute the matrix elements that arise in the Krylov iterations, we employ a Feynman diagrammatic representation that is then evaluated with Monte Carlo techniques. Each order of the Krylov iteration is variational and is guaranteed to improve upon the previous iteration. The first Krylov iteration is akin to the NLO approach of Elias-Mir\'o et al. \cite{Elias-Miro:2017tup}. To demonstrate this approach, we focus on the $1+1d$ dimensional $\phi^4$ model and compute the bulk energy and mass gaps in both the $\mathbb{Z}_2$-broken and unbroken sectors. We estimate the critical $\phi^4$ coupling in the broken phase to be $g_c=0.2645\pm0.002$., Comment: 33 pages, 21 figures, 4 tables

We study the time-dependent response of a Heisenberg spin ladder subjected to a time-dependent square form variation of its rung spin exchange coupling. To do so, we employ a field theoretic representation of the Heisenberg spin ladder consisting of a singlet and a triplet of Majorana fermions. Because this underlying description is free fermionic, we are able to develop closed form analytic expressions for dynamical quantities, both one-body measures of local spin correlations as well as two-time correlation functions. These expressions involve both the gaps to triplet and singlet excitations. We analyze these expressions obtaining both the time scales for their transients and long-time athermal steady state behaviors. We show that variations in the rung coupling are directly tied to changes in the local antiferromagnetic correlations. We further discuss the application of these results to pump-probe experiments on material realizations of low-dimensional magnetic systems., Comment: 62 pages, 15 figures; References updated; Copyright information updated

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model., Comment: 48 pages, 6 figures, v2: minor revision with two new Appendices

We consider the problem of the development of steady states in one-dimensional Bose gas tubes that are weakly coupled to one another through a density-density interaction. We analyze this development through a Boltzmann collision integral approach. We argue that when the leading order of the collision integral, where single particle-hole excitations are created in individual gases, is dominant, the state of the gas evolves first to a non-thermal fixed point, i.e. a prethermalization plateau. This order is dominant when a pair of tubes are inequivalent with, say, different temperatures or different effective interaction parameters, $\gamma$. We characterize this non-thermal prethermalization plateau, constructing both the quasi-conserved quantities that control the existence of this plateau as well as the associated generalized Gibbs ensemble., Comment: 40 pages, 9 figures, new version with improved discussion of conserved charges

Simple and fast analytic method to find out optimal combinations of sizes of neutron moderator and optical system entrance, allowing for the full sample illumination with minimum to none background, is developed. In the case of employing low-dimensional para-hydrogen moderators with enhanced neutron beam brilliance, the method allows to determine the minimum size of moderator, which provides the highest sample flux while keeping the sample fully illuminated. This method can be used during the design of new neutron sources, upgrades of neutron optical systems and moderator replacements., Comment: 38 pages, 20 figures

We propose a framework to jointly determine the deformation parameters and reconstruct the unknown volume in electron cryotomography (CryoET). CryoET aims to reconstruct three-dimensional biological samples from two-dimensional projections. A major challenge is that we can only acquire projections for a limited range of tilts, and that each projection undergoes an unknown deformation during acquisition. Not accounting for these deformations results in poor reconstruction. The existing CryoET software packages attempt to align the projections, often in a workflow which uses manual feedback. Our proposed method sidesteps this inconvenience by automatically computing a set of undeformed projections while simultaneously reconstructing the unknown volume. We achieve this by learning a continuous representation of the undeformed measurements and deformation parameters. We show that our approach enables the recovery of high-frequency details that are destroyed without accounting for deformations.

Chromosome analysis is essential for diagnosing genetic disorders. For hematologic malignancies, identification of somatic clonal aberrations by karyotype analysis remains the standard of care. However, karyotyping is costly and time-consuming because of the largely manual process and the expertise required in identifying and annotating aberrations. Efforts to automate karyotype analysis to date fell short in aberration detection. Using a training set of ~10k patient specimens and ~50k karyograms from over 5 years from the Fred Hutchinson Cancer Center, we created a labeled set of images representing individual chromosomes. These individual chromosomes were used to train and assess deep learning models for classifying the 24 human chromosomes and identifying chromosomal aberrations. The top-accuracy models utilized the recently introduced Topological Vision Transformers (TopViTs) with 2-level-block-Toeplitz masking, to incorporate structural inductive bias. TopViT outperformed CNN (Inception) models with >99.3% accuracy for chromosome identification, and exhibited accuracies >99% for aberration detection in most aberrations. Notably, we were able to show high-quality performance even in "few shot" learning scenarios. Incorporating the definition of clonality substantially improved both precision and recall (sensitivity). When applied to "zero shot" scenarios, the model captured aberrations without training, with perfect precision at >50% recall. Together these results show that modern deep learning models can approach expert-level performance for chromosome aberration detection. To our knowledge, this is the first study demonstrating the downstream effectiveness of TopViTs. These results open up exciting opportunities for not only expediting patient results but providing a scalable technology for early screening of low-abundance chromosomal lesions.

We propose a differentiable imaging framework to address uncertainty in measurement coordinates such as sensor locations and projection angles. We formulate the problem as measurement interpolation at unknown nodes supervised through the forward operator. To solve it we apply implicit neural networks, also known as neural fields, which are naturally differentiable with respect to the input coordinates. We also develop differentiable spline interpolators which perform as well as neural networks, require less time to optimize and have well-understood properties. Differentiability is key as it allows us to jointly fit a measurement representation, optimize over the uncertain measurement coordinates, and perform image reconstruction which in turn ensures consistent calibration. We apply our approach to 2D and 3D computed tomography, and show that it produces improved reconstructions compared to baselines that do not account for the lack of calibration. The flexibility of the proposed framework makes it easy to extend to almost arbitrary imaging problems.

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intra-chain interactions and the weak interchain coupling. When the intra-chain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. We find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally non-exponential, even for spatially uniform perturbations., Comment: v2: improved presentation, 6 pages + 15 pages of supplemental materials

Most deep learning models for computational imaging regress a single reconstructed image. In practice, however, ill-posedness, nonlinearity, model mismatch, and noise often conspire to make such point estimates misleading or insufficient. The Bayesian approach models images and (noisy) measurements as jointly distributed random vectors and aims to approximate the posterior distribution of unknowns. Recent variational inference methods based on conditional normalizing flows are a promising alternative to traditional MCMC methods, but they come with drawbacks: excessive memory and compute demands for moderate to high resolution images and underwhelming performance on hard nonlinear problems. In this work, we propose C-Trumpets -- conditional injective flows specifically designed for imaging problems, which greatly diminish these challenges. Injectivity reduces memory footprint and training time while low-dimensional latent space together with architectural innovations like fixed-volume-change layers and skip-connection revnet layers, C-Trumpets outperform regular conditional flow models on a variety of imaging and image restoration tasks, including limited-view CT and nonlinear inverse scattering, with a lower compute and memory budget. C-Trumpets enable fast approximation of point estimates like MMSE or MAP as well as physically-meaningful uncertainty quantification., Comment: 23 pages, 23 figures

We review the solution of QCD in two spacetime dimensions. Following the analysis of Baluni, for a single flavor the model can be analyzed using Abelian bosonization. The theory can be analyzed in strong coupling, when the quarks are much lighter than the gauge coupling. In this limit, the theory is given by a Luttinger liquid., Comment: Submitted by R.D.P. to the journal Universe as part of the Special Issue "keV Warm Dark Matter ({\Lambda}WDM) in Agreement with Observations, in Tribute to H\'ector J. De Vega"

We analyze the behavior of quarks coupled to a $SU(N_c)$ gauge theory in 1+1 dimensions. In the limit of strong coupling, the model reduces to a Wess-Zumino-Novikov-Witten (WZNW) model. At nonzero density, excitations near the Fermi surface form a non-Fermi liquid. With $N_f$ flavors, the finite density of quarks reduce to a free $U(1)$ field, which governs fluctuations in baryon number, together with a WZNW $SU(N_f)$ nonlinear sigma model at level $N_c$, from the pion/kaon modes. We compute the singularity in the charge susceptibility at the Fermi surface and the attendant power law correlations. We suggest that this is relevant to the quarkyonic regime of cold, dense QCD in 3+1 dimensions, in the limit that the Fermi surface is covered by many small patches, and the theory is effectively one dimensional. In this regime the dominant excitations near the Fermi surface are not baryons, but gapless bosonic modes.

We introduce and study generalized R\'enyi entropies defined through the traces of products of ${\rm Tr}_B (|\Psi_i\rangle\langle \Psi_j|)$ where $|\Psi_i\rangle$ are eigenstates of a two-dimensional conformal field theory (CFT). When $|\Psi_i\rangle=|\Psi_j\rangle$ these objects reduce to the standard R\'enyi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized R\'enyi entropies are equivalent to four-point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized R\'enyi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard R\'enyi and relative entropies involving arbitrary descendent states of the bosonic CFT., Comment: 29 pages, 4 figures, published version

The growth of Renyi entropies after the injection of energy into a correlated system provides a window upon the dynamics of its entanglement properties. We develop here a simulation scheme by which this growth can be determined in Luttinger liquids systems with arbitrary interactions, even those introducing gaps into the liquid. We apply this scheme to an experimentally relevant quench in the sine-Gordon field theory. While for short times we provide an analytic expression for the growth of the second and third Renyi entropy, to access longer times, we combine our scheme with truncated spectrum methods., Comment: 6 pages, 3 figures; Suppl. Mat.: 16 pages, 8 figures, v3: Improved version of the manuscript

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, $\sigma(x)$ and $\sigma'(x)$, in either phase are accompanied by associated disorder operators, $\mu(x)$ and $\mu'(x)$. Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For $\sigma(x)$ and $\sigma'(x)$, the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest $\mathbb{Z}_2$ odd particles. Similarly, the equations for $\mu(x)$ and $\mu'(x)$ have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for $\sigma(x)/\sigma'(x)$ are fixed in terms of those for $\mu(x)/\mu'(x)$. We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the $\Delta$-sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments., Comment: v2: typos corrected, some details clarified, references added, tables and figures updated. v3: some more details clarified, typos corrected

We employ variational autoencoders to extract physical insight from a dataset of one-particle Anderson impurity model spectral functions. Autoencoders are trained to find a low-dimensional, latent space representation that faithfully characterizes each element of the training set, as measured by a reconstruction error. Variational autoencoders, a probabilistic generalization of standard autoencoders, further condition the learned latent space to promote highly interpretable features. In our study, we find that the learned latent variables strongly correlate with well known, but nontrivial, parameters that characterize emergent behaviors in the Anderson impurity model. In particular, one latent variable correlates with particle-hole asymmetry, while another is in near one-to-one correspondence with the Kondo temperature, a dynamically generated low-energy scale in the impurity model. Using symbolic regression, we model this variable as a function of the known bare physical input parameters and "rediscover" the non-perturbative formula for the Kondo temperature. The machine learning pipeline we develop suggests a general purpose approach which opens opportunities to discover new domain knowledge in other physical systems., Comment: Update to match PRB publication + typo fixes + minor edits

Building on previous developments, we show that the Diagrammatic Monte Carlo technique allows to compute finite temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon line-width in a homogeneous electron gas (jellium)., Comment: 5 pages and 5 figures in the main text plus 7 pages and 7 figures in the Supplemental material

We propose injective generative models called Trumpets that generalize invertible normalizing flows. The proposed generators progressively increase dimension from a low-dimensional latent space. We demonstrate that Trumpets can be trained orders of magnitudes faster than standard flows while yielding samples of comparable or better quality. They retain many of the advantages of the standard flows such as training based on maximum likelihood and a fast, exact inverse of the generator. Since Trumpets are injective and have fast inverses, they can be effectively used for downstream Bayesian inference. To wit, we use Trumpet priors for maximum a posteriori estimation in the context of image reconstruction from compressive measurements, outperforming competitive baselines in terms of reconstruction quality and speed. We then propose an efficient method for posterior characterization and uncertainty quantification with Trumpets by taking advantage of the low-dimensional latent space., Comment: 16 pages

The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410k and 600k spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with point-wise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of $10^5$ over traditional AIM solvers. The required size of the training set of our model can be significantly reduced using furthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multi-channel impurity problems of relevance to predicting the properties of real materials., Comment: 31 pages, 27 figures, 5 tables

Disentangling the primary order parameter from secondary order parameters in phase transitions is critical to the interpretation of the transition mechanisms in strongly correlated systems and quantum materials. Here we present a study of structural phase transition pathways in superionic Cu2S nanocrystals that exhibit intriguing properties. Utilizing ultrafast electron diffraction techniques sensitive in both momentum-space and the time-domain, we distinguish the dynamics of crystal symmetry breaking and lattice expansion in this system. We are able to follow the transient states along the transition pathway and so observe the dynamics of both the primary and secondary order parameters. Based on these observations we argue that the mechanism of the structural phase transition in Cu2S is dominated by the electron-phonon coupling. This mechanism advances the understanding from previous results where the focus was solely on dynamic observations of the lattice expansion.

One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the $b \rightarrow 1/b$ self-duality of its $S$-matrix, of which there is no trace in its Lagrangian formulation. Here $b$ is the coupling appearing in the model's eponymous hyperbolic cosine present in its Lagrangian, $\cosh(b\phi)$. In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for $b \ll 1$ and intermediate values of $b$, but as the self-dual point $b=1$ is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff $E_c$ dependence, which disappears according only to a very slow power law in $E_c$. Standard renormalization group strategies -- whether they be numerical or analytic -- also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of $b=1$. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how `quantum mechanical' vs `quantum field theoretic' the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of $b$ as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase $b > 1$ of the Lagrangian formulation of model may be different from what is na\"ively inferred from its $S$-matrix. In particular, we present an argument that the theory is massless for $b>1$., Comment: 84 pages, 23 figures, 1 table

Injectivity plays an important role in generative models where it enables inference; in inverse problems and compressed sensing with generative priors it is a precursor to well posedness. We establish sharp characterizations of injectivity of fully-connected and convolutional ReLU layers and networks. First, through a layerwise analysis, we show that an expansivity factor of two is necessary and sufficient for injectivity by constructing appropriate weight matrices. We show that global injectivity with iid Gaussian matrices, a commonly used tractable model, requires larger expansivity between 3.4 and 10.5. We also characterize the stability of inverting an injective network via worst-case Lipschitz constants of the inverse. We then use arguments from differential topology to study injectivity of deep networks and prove that any Lipschitz map can be approximated by an injective ReLU network. Finally, using an argument based on random projections, we show that an end-to-end -- rather than layerwise -- doubling of the dimension suffices for injectivity. Our results establish a theoretical basis for the study of nonlinear inverse and inference problems using neural networks., Comment: 48 pages, 18 figures, submitted to JMLR

We propose a general physics-based deep learning architecture for wave-based imaging problems. A key difficulty in imaging problems with a varying background wave speed is that the medium "bends" the waves differently depending on their position and direction. This space-bending geometry makes the equivariance to translations of convolutional networks an undesired inductive bias. We build an interpretable neural architecture inspired by Fourier integral operators (FIOs) which approximate the wave physics. FIOs model a wide range of imaging modalities, from seismology and radar to Doppler and ultrasound. We focus on learning the geometry of wave propagation captured by FIOs, which is implicit in the data, via a loss based on optimal transport. The proposed FIONet performs significantly better than the usual baselines on a number of imaging inverse problems, especially in out-of-distribution tests., Comment: Accepted as spotlight presentation to NeurIPS '20

Micro-expressions are brief and subtle facial expressions that go on and off the face in a fraction of a second. This kind of facial expressions usually occurs in high stake situations and is considered to reflect a human's real intent. There has been some interest in micro-expression analysis, however, a great majority of the methods are based on classically established computer vision methods such as local binary patterns, histogram of gradients and optical flow. A novel methodology for micro-expression recognition using the Riesz pyramid, a multi-scale steerable Hilbert transform is presented. In fact, an image sequence is transformed with this tool, then the image phase variations are extracted and filtered as proxies for motion. Furthermore, the dominant orientation constancy from the Riesz transform is exploited to average the micro-expression sequence into an image pair. Based on that, the Mean Oriented Riesz Feature description is introduced. Finally the performance of our methods are tested in two spontaneous micro-expressions databases and compared to state-of-the-art methods.

We study how multiple charge excitations appear in the resonant inelastic x-ray scattering (RIXS) spectra of metals. The single excitations in the problem are the plasmons and electron-hole pairs, and multi-excitation processes are usually neglected. However, at small momentum transfer the multi-excitation contributions may dominate the signal and one needs to understand how to interpret the data. In particular, we demonstrate how to "decode" the total multi-excitation intensity and extract the plasmon dispersion. While our calculations are based on the random phase approximation, which does not allow to obtain quantitatively precise results in the entire region of parameters, we expect them to capture semi-qualitatively all features expected for charged Fermi-liquid states, including universal and singular properties of the RIXS spectra., Comment: 10 pages, 19 figures

Although ultrafast manipulation of magnetism holds great promise for new physical phenomena and applications, targeting specific states is held back by our limited understanding of how magnetic correlations evolve on ultrafast timescales. Using ultrafast resonant inelastic x-ray scattering we demonstrate that femtosecond laser pulses can excite transient magnons at large wavevectors in gapped antiferromagnets, and that they persist for several picoseconds which is opposite to what is observed in nearly gapless magnets. Our work suggests that materials with isotropic magnetic interactions are preferred to achieve rapid manipulation of magnetism., Comment: 6 pages, 4 figures, not including supplemental material; accepted in PNAS

We develop a formalism to study the Resonant Inelastic X-ray Scattering (RIXS) response in metals based on the diagrammatic expansion for its cross section. The standard approach to the solution of the RIXS problem relies on two key approximations: short-range potentials and non-interacting conduction electrons. However, these approximations are inaccurate for charged particles in metals, where the long-range Coulomb interaction and dynamic screening effects are very important. In this work we study how to extract important information about collective excitations in the Coulomb plasma, plasmons and electron-hole pairs, from RIXS data. We find that single- and multi-plasmon excitations can easily be distinguished by positions of the corresponding peaks, singularities, and their intensities. We also discuss the hybrid processes, where plasmon emission is accompanied by excitation of electron-hole pairs, and study how they manifest themselves., Comment: 5 pages, 5 figures, Appendix

The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in the angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an interacting one-dimensional Bose gas, the Lieb-Linger model, the dynamical localization can persist., Comment: 5 pages, 2 figures

There is a dichotomy in the nonequilibrium dynamics of quantum many body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new `meson' excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously., Comment: v1: 29 pages, 26 figures; v2: 31 pages, 27 figures (as published)

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our work is that in practice they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications., Comment: 14 pages, 12 figures

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and because we can only get few measurements. This setting is common in geophysical imaging and remote sensing. We show that in this case the common approach to directly learn the mapping from the measured data to the reconstruction becomes unstable. Instead, we propose to first learn an ensemble of simpler mappings from the data to projections of the unknown image into random piecewise-constant subspaces. We then combine the projections to form a final reconstruction by solving a deconvolution-like problem. We show experimentally that the proposed method is more robust to measurement noise and corruptions not seen during training than a directly learned inverse., Comment: S. Gupta and K. Kothari contributed equally

We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete 'meson' modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy $E$ do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two meson threshold, due to a surprising lack of hybridization with the ($n\geq4$)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous post-quench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. The nonthermal states are confined to the ordered phase - the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability., Comment: 15 pages (of which 11 are appendices). 8 figures

Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900, 2006], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the one-dimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges., Comment: v1: 7+10 pages, 3+7 figures. v2: references added, pictures with refined discretization. v3: addition of discussion of integrability breaking by trap + small improvements

We consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form., Comment: 18 pages, 7 figures

Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times, these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations., Comment: 17 pages + appendices

The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-ABACUS algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes., Comment: v1: 6+7 pages, 4 figures. v2: 6+9 pages, 7 figures. References added, discussion improved, title changed. v3: 6+9 pages, 7 figures, discussion further improved, references added

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics., Comment: 111 pages, 54 figures, 6 tables; comments welcome

We study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang-Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at $2k_F$ and a finite-momentum roton minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as $1/L$ for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the $2k_F$ gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang-Gaudin Bose gas is also host to multi-spinon bound states, known as $\Lambda$-strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length $n$ $\Lambda$-string dressed energies $\epsilon_n(\lambda)$ and the dressed energy $\epsilon(k)$. We solve the Yang-Yang-Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length $n$ $\Lambda$-string dressed energy is Lorentzian over a wide range of real string centers $\lambda$ in the vicinity of $\lambda = 0$. We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations., Comment: v1 31 pages, 12 figures; v2 33 pages, 13 figures, as accepted

Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic x-ray scattering (RIXS) to follow the evolution of charge correlations in the canonical stripe ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ (LBCO~$1/8$) across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates., Comment: Accepted in Proceeding of the National Academy of Sciences; 8 pages, 4 figures