Search

The Hatano-Nelson (HN) Hamiltonian has played a pivotal role in catalyzing research interest in non-Hermitian systems, primarily because it showcases unique physical phenomena that arise solely due to non-Hermiticity. The non-Hermiticity in the HN Hamiltonian, driven by asymmetric hopping amplitudes, induces a delocalization-localization (DL) transition in a one-dimensional (1D) lattice with random disorder, sharply contrasting with its Hermitian counterpart. A similar DL transition occurs in a 1D quasiperiodic HN (QHN) lattice, where a critical quasiperiodic potential strength separates metallic and insulating states, akin to the Hermitian case. In these systems, all states below the critical potential are delocalized, while those above are localized. In this study, we reveal that coupling two 1D QHN lattices can significantly alter the nature of the DL transition. We identify two critical points, $V_{c1} < V_{c2}$, when the nearest neighbors of the two 1D QHN lattices are cross-coupled with strong hopping amplitudes under periodic boundary conditions (PBC). Generally, all states are completely delocalized below $ V_{c1}$ and completely localized above $V_{c2}$, while two mobility edges symmetrically emerge about $\rm{Re[E]} = 0$ between $V_{c1}$ and $V_{c2}$. Notably, under specific asymmetric cross-hopping amplitudes, $V_{c1}$ approaches zero, resulting in localized states even for infinitesimally weak potential. Remarkably, we also find that the mobility edges precisely divide the delocalized and localized states in equal proportions. Furthermore, we observe that the conventional one-to-one correspondence between electronic states under PBC and open boundary conditions (OBC) in 1D HN lattices breaks, Comment: 7 pages, 5 figures

During development and under normal physiological conditions, biological tissues are continuously subjected to substantial mechanical stresses. In response to large deformations cells in a tissue must undergo multicellular rearrangements in order to maintain integrity and robustness. However, how these events are connected in time and space remains unknown. Here, using computational and theoretical modeling, we studied the mechanical plasticity of epithelial monolayers under large deformations. Our results demonstrate that the jamming-unjamming (solid-fluid) transition in tissues can vary significantly depending on the degree of deformation, implying that tissues are highly unconventional materials. Using analytical modeling, we elucidate the origins of this behavior. We also demonstrate how a tissue accommodates large deformations through a collective series of rearrangements, which behave similarly to avalanches in non-living materials. We find that these tissue avalanches are governed by stress redistribution and the spatial distribution of vulnerable spots. Finally, we propose a simple and experimentally accessible framework to predict avalanches and infer tissue mechanical stress based on static images.

We study a lattice model describing the non-equilibrium dynamics emerging from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry pertinent for the investigation of confinement-induced effects. We analytically derive exact results for the characteristic function of the moments valid to first order in the obstacle density. By calculating the velocity autocorrelation function and its long-time tail we find that already in equilibrium the system exhibits a dimensional crossover. This picture is further confirmed by the approach of the drift velocity to its terminal value attained in the non-equilibrium stationary state. At large times the diffusion coefficient is affected by both the driving and confinement in a way that we quantify analytically. The force-induced diffusion coefficient depends sensitively on the presence of confinement. The latter is able to modify qualitatively the non-analytic behavior in the force observed for the unbounded model. We then examine the fluctuations of the tracer particle along the driving force. We show that in the intermediate regime superdiffusive anomalous behavior persists even in the presence of confinement. Stochastic simulations are employed in order to test the validity of the analytic results, exact to first order in the obstacle density and valid for arbitrary force and confinement., Comment: 24 pages, 7 figures

We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a cylinder. We compute the velocity autocorrelation function and show that already in equilibrium the system exhibits a dimensional crossover from two- to one-dimensional as time progresses. A pulling force is switched on and we characterize analytically the stationary state in terms of the stationary velocity and diffusion coefficient. Stochastic simulations are used to discuss the range of validity of the analytic results. Our calculation, exact to first order in the obstacle density, holds for arbitrarily large forces and confinement size., Comment: 6 pages, 3 figures

With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate, financial, ecological, and neural systems. The underlying mechanisms are commonly encoded into network structures, e.g., capturing how constituents interact with each other to produce emergent behavior. Here, we address whether a good network reconstruction suggests a good dynamics prediction. The answer is quite dependent on the nature of the supplied (observed) dynamics sequences measured on the complex system. When the dynamics are not chaotic, network reconstruction implies dynamics prediction. In contrast, even if a network can be well reconstructed from the chaotic time series (chaos means that many unstable dynamics states coexist), the prediction of the future dynamics can become impossible as at some future point the prediction error will be amplified. This is explained by using dynamical mean-field theory on a toy model of random recurrent neural networks., Comment: 27 pages, 9 figures

The Master Stability Function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic dynamical systems, its application to periodic systems has been less explored. By studying several well-known periodic systems, we establish a comprehensive framework to understand and classify their properties of synchronizability. This allows us to define five distinct classes of synchronization stability, including some that are unique to periodic systems. Specifically, in periodic systems, the Master Stability Function vanishes at the origin, and it can therefore display behavioral classes that are not achievable in chaotic systems, where it starts, instead, at a strictly positive value. Moreover, our results challenge the widely-held belief that periodic systems are easily put in a stable synchronous state, showing, instead, the common occurrence of a lower threshold for synchronization stability., Comment: 8 pages, 6 figures, plus supplementary material with 5 pages and 6 figures

We begin with an exact expression for the entropy of a system of hard spheres within the Hamming space. This entropy relies on probability marginals, which are determined by an extended set of Belief Propagation (BP) equations. The BP probability marginals are functions of auxiliary variables which are introduced to model the effects of loopy interactions on a tree-structured interaction graph. We explore various reasonable and approximate probability distributions, ensuring they align with the exact solutions of the BP equations. Our approach is based on an ansatz of (in)homogeneous cavity marginals respecting the permutation symmetry of the problem. Through thorough analysis, we aim to minimize errors in the BP equations. Our findings support the conjecture that the maximum packing density asymptotically conforms to the lower bound proposed by Gilbert and Varshamov, further validated by the solution of the loopy BP equations., Comment: 31 pages, 4 figures

Quantum reservoir computing (QRC) is a low-complexity learning paradigm that combines the inherent dynamics of input-driven many-body quantum systems with classical learning techniques for nonlinear temporal data processing. Optimizing the QRC process and computing device is a complex task due to the dependence of many-body quantum systems to various factors. To explore this, we introduce a strongly interacting spin model on random regular graphs as the quantum component and investigate the interplay between static disorder, interactions, and graph connectivity, revealing their critical impact on quantum memory capacity and learnability accuracy. We tackle linear quantum and nonlinear classical tasks, and identify optimal learning and memory regimes through studying information localization, dynamical quantum correlations, and the many-body structure of the disordered Hamiltonian. In particular, we uncover the role of previously overlooked network connectivity and demonstrate how the presence of quantum correlations can significantly enhance the learning performance. Our findings thus provide guidelines for the optimal design of disordered analog quantum learning platforms.

Quantum complexity has emerged as a central concept in diverse areas of physics, ranging from quantum computing to the theory of black holes. We perform a systematic study of complexity in random quantum circuits with and without measurements. We observe that complexity grows linearly before saturating to a constant value. For $N$ qubits without measurements, the saturation value scales as $2^{N-1}$, and the saturation time scales as $2^N$. This behaviour remains identical in the presence of random measurements with different probabilities, indicating that this notion of complexity is insensitive to the rate of measurement. We also study the behaviour of complexity in two variants of the random unitary floquet circuit, where we observe that complexity acts as a novel probe of Anderson localization and many-body localization., Comment: 6 pages, 3 figures

Recent research has made significant progress in understanding localization transitions and mobility edges (MEs) that separate extended and localized states in non-Hermitian (NH) quasicrystals. Here we focus on studying critical states and anomalous MEs, which identify the boundaries between critical and localized states within two distinct NH quasiperiodic models. Specifically, the first model is a quasiperiodic mosaic lattice with both nonreciprocal hopping term and on-site potential. In contrast, the second model features an unbounded quasiperiodic on-site potential and nonreciprocal hopping. Using Avila's global theory, we analytically derive the Lyapunov exponent and exact anomalous MEs. To confirm the emergence of the robust critical states in both models, we conduct a numerical multifractal analysis of the wave functions and spectrum analysis of level spacing. Furthermore, we investigate the transition between real and complex spectra and the topological origins of the anomalous MEs. Our results may shed light on exploring the critical states and anomalous MEs in NH quasiperiodic systems.

We propose algorithms for addressing the bias of the posterior mean when used as an estimator of parameters. These algorithms build upon the recently proposed Bayesian infinitesimal jackknife approximation (Giordano and Broderick (2023)) and can be implemented using the posterior covariance and third-order combined cumulants easily calculated from MCMC outputs. Two algorithms are introduced: The first algorithm utilises the output of a single-run MCMC with the original likelihood and prior to estimate the bias. A notable feature of the algorithm is that its ability to estimate definitional bias (Efron (2015)), which is crucial for Bayesian estimators. The second algorithm is designed for high-dimensional and sparse data settings, where ``quasi-prior'' for bias correction is introduced. The quasi-prior is iteratively refined using the output of the first algorithm as a measure of the residual bias at each step. These algorithms have been successfully implemented and tested for parameter estimation in the Weibull distribution and logistic regression in moderately high-dimensional settings.

Understanding the flow dynamics of yield stress fluids in porous media presents a substantial challenge. Both experiments and extensive numerical simulations frequently show a non-linear relationship between the flow rate and the pressure gradient, deviating from the traditional Darcy law. In this article, we consider a tree-like porous structure and utilize an exact mapping with the directed polymer (DP) with disordered bond energies on the Cayley tree. Specifically, we adapt an algorithm recently introduced by Brunet et al. [Europhys. Lett. 131, 40002 (2020)] to simulate exactly the tip region of branching random walks with the help of a spinal decomposition, to accurately compute the flow on extensive trees with several thousand generations. Our results confirm the asymptotic predictions proposed by Schimmenti et al. [Phys. Rev. E 108, L023102 (2023)], tested therein only for moderate trees of about 20 generations., Comment: 23 pages, 10 figures

The performance of quantum error correcting (QEC) codes are often studied under the assumption of spatio-temporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. In this work, we study effects of non-uniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatio-temporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code., Comment: 22 pages, 17 figures

This paper deals with themes such as approximate counting/evaluation of the total number of flat-foldings for random origami diagrams, evaluation of the values averaged over various instances, obtaining forcing sets for general origami diagrams, and evaluation of average computational complexity. An approach to the above problems using a physical model and an efficient size reduction method for them is proposed. Using a statistical mechanics model and a numerical method of approximate enumeration based on it, we give the result of approximate enumeration of the total number of flat-foldings of single-vertex origami diagram with random width of angles gathering around the central vertex, and obtain its size dependence for an asymptotic prediction towards the limit of infinite size. In addition, an outlook with respect to the chained determination of local stacking orders of facets caused by the constraint that prohibits the penetration of them is also provided from the viewpoint of organizing the terms included in the physical model. A method to efficiently solve the problem of the determination or enumeration of flat-foldings is discussed based on the above perspectives. This is thought to be closely related to forcing sets., Comment: 16 pages, 11 figures. Submitted to Origami8: Proceedings of the 8th International Meeting on Origami in Science, Mathematics and Education (8OSME), Melbourne, August 16-18, 2024

The recent surge in Generative Artificial Intelligence (AI) has introduced exciting possibilities for computational chemistry. Generative AI methods have made significant progress in sampling molecular structures across chemical species, developing force fields, and speeding up simulations. This Perspective offers a structured overview, beginning with the fundamental theoretical concepts in both Generative AI and computational chemistry. It then covers widely used Generative AI methods, including autoencoders, generative adversarial networks, reinforcement learning, flow models and language models, and highlights their selected applications in diverse areas including force field development, and protein/RNA structure prediction. A key focus is on the challenges these methods face before they become truly predictive, particularly in predicting emergent chemical phenomena. We believe that the ultimate goal of a simulation method or theory is to predict phenomena not seen before, and that Generative AI should be subject to these same standards before it is deemed useful for chemistry. We suggest that to overcome these challenges, future AI models need to integrate core chemical principles, especially from statistical mechanics.

Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion can be applied to systematically improve the accuracy of a BP approximation to a tensor network contraction, in principle converging arbitrarily close to the exact result. More generally, our result provides a framework for expanding a tensor network as a sum of component networks in a hierarchy of increasing complexity. We benchmark this proposal for the contraction of iPEPS, either representing the ground state of an AKLT model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude whilst incurring only a minor increase in computational cost. These results indicate that the proposed series expansions could be a useful tool to accurately evaluate tensor networks in cases that otherwise exceed the limits of established contraction routines., Comment: 13 pages, 10 figures

The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as powerful tools to complement these standard approaches, offering valuable insights into phase and structure determination. Additionally, they have been shown to enhance the application of traditional methods. In this work, we review recent advancements in this area, with a focus on our contributions to phase and structure determination using supervised and unsupervised learning methods in several systems: (a) 2D site percolation, (b) the 3D Anderson model of localization, (c) the 2D $J_1$-$J_2$ Ising model, and (d) the prediction of large-angle convergent beam electron diffraction patterns., Comment: 15 two-column pages and 8 figures, invited review to the JPSJ issue of Special Topics "Machine Learning Physics"

We propose a new Floquet time crystal model that responds in arbitrary multiples of the driving period. Such an n-tuple discrete time crystal is theoretically constructed by permuting spins in a disordered chain and is well suited for experiment implementations. Transitions between these time crystals with different periods give rise to a novel phase of matter that we call subspace-thermal discrete time crystals, where states within subspaces are fully thermalized at an early time. However, the whole system still robustly responds to the periodic driving subharmonically, with a period being the greatest common divisor of the original two periods. Existing theoretical analysis from many-body localization fails to understand the rigidity of such subspace-thermal time crystal phases. To resolve this, we develop a new theoretical framework from the perspective of the robust $2\pi/n$ quasi-energy gap. Its robustness is analytically proved, under a reasonable conjecture, by a new perturbation theory for unitary operators. The proof applies beyond the models considered here to other existing discrete time crystals realized by kicking disordered systems, thus offering a systematic way to construct new discrete time crystal models. We also introduce the notion of DTC-charges that allow us to probe the observables that spontaneously break the time-translation symmetry in both the regular discrete time crystals and subspace-thermal discrete time crystals. Moreover, our discrete time crystal models can be generalized to higher spin magnitudes or qudits, as well as higher spatial dimensions., Comment: 30 pages, 7 figures

We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasi-polynomial runtime for inverse temperatures up to $\beta={\rm poly}(\ln(n))$. At the core of our approach is the Density Matrix Renormalization Group algorithm, which typically does not guarantee efficiency. We have created a new truncation scheme for the matrix product operator of the quantum Gibbs states, which allows us to control the error analytically. Additionally, our method is applied to simulate the time evolution of systems with long-range interactions, achieving significantly better precision than that offered by the Lieb-Robinson bound., Comment: 7 pages + 9 pages Supplementary materials, 1 figure

The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models. In this paper we aim to address a gap in the literature, namely, to examine how gradual improvement of power grid models affect the goodness of certain metrics. To study how the details of models are perceived by the different metrics, 12 variations of a power grid model were created, introducing varying level of heterogeneity through the coupling strength, the nodal powers and the moment of inertia. The grid models were compared using a second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the values of the phase, the frequency and the universal order parameters. Finally, frequency results of the models were compared to grid measurements. We found that the universal order parameter was able to capture more details of the grid models, especially in cases of decreasing moment of inertia. The most heterogeneous models showed very low synchronization and thus suggest a limitation of the second-order Kuramoto equation. Finally, we show local frequency results related to the multi-peaks of static models, which implies that spatial heterogeneity can also induce such multi-peak behavior., Comment: 7 pages, 7 figures

The effects of noise on memory in a linear recurrent network are theoretically investigated. Memory is characterized by its ability to store previous inputs in its instantaneous state of network, which receives a correlated or uncorrelated noise. Two major properties are revealed: First, the memory reduced by noise is uniquely determined by the noise's power spectral density (PSD). Second, the memory will not decrease regardless of noise intensity if the PSD is in a certain class of distribution (including power law). The results are verified using the human brain signals, showing good agreement.

We consider the effects of weak measurements on the quantum critical ground state of the one-dimensional (a) tricritical and (b) critical quantum Ising model, by measuring in (a) the local energy and in (b) the local spin operator in a lattice formulation. By employing a controlled renormalization group (RG) analysis we find that each problem exhibits highly complex novel scaling behavior, arising from the intrinsically indeterministic ('random') nature of quantum mechanical measurements, which is governed by a measurement-dominated RG fixed point that we study within an $\epsilon$ expansion. In the tricritical Ising case (a) we find (i): multifractal scaling behavior of energy and spin correlations in the measured groundstate, corresponding to an infinite hierarchy of independent critical exponents and, equivalently, to a continuum of universal scaling exponents for each of these correlations; (ii): the presence of logarithmic factors multiplying powerlaws in correlation functions, a hallmark of 'logarithmic conformal field theories' (CFT); (iii): universal 'effective central charges' $c^{({\rm eff})}_n$ for the prefactors of the logarithm of subsystem size of the $n$th R\'enyi entropies, which are independent of each other for different $n$, in contrast to the unmeasured critical ground state, and (iv): a universal ("Affleck-Ludwig") 'effective boundary entropy' $S_{\rm{eff}}$ which we show, quite generally, to be related to the system-size independent part of the Shannon entropy of the measurement record, computed explicitly here to 1-loop order. - A subset of these results have so-far also been obtained within the $\epsilon$ expansion for the measurement-dominated critical point in the critical Ising case (b)., Comment: 37 pages, 4 figures, 1 table

Higher loading of active electrode materials is desired in batteries, especially those based on conversion reactions, for enhanced energy density and cost efficiency. However, increasing active material loading in electrodes can cause significant performance depreciation due to internal resistance, shuttling, and parasitic side reactions, which can be alleviated to a certain extent by a compatible design of electrolytes. In this work, a data-driven approach is leveraged to find a high-performing electrolyte formulation for a novel interhalogen battery custom to the target cathode loading. An electrolyte design consisting of 4 solvents and 4 salts is experimentally devised for a novel interhalogen battery based on a multi-electron redox reaction. The experimental dataset with variable electrolyte compositions and active cathode loading, is used to train a graph-based deep learning model mapping changing variables in the battery's material design to its specific capacity. The trained model is used to further optimize the electrolyte formulation compositions for enhancing the battery capacity at a target cathode loading by a two-fold approach: large-scale screening and interpreting electrolyte design principles for different cathode loadings. The data-driven approach is demonstrated to bring about an additional 20% increment in the specific capacity of the battery over capacities obtained from the experimental optimization., Comment: 34 Pages, 5 Figures, 2 Tables

We develop a theory to analyze how structure in connectivity shapes the high-dimensional, internally generated activity of nonlinear recurrent neural networks. Using two complementary methods -- a path-integral calculation of fluctuations around the saddle point, and a recently introduced two-site cavity approach -- we derive analytic expressions that characterize important features of collective activity, including its dimensionality and temporal correlations. To model structure in the coupling matrices of real neural circuits, such as synaptic connectomes obtained through electron microscopy, we introduce the random-mode model, which parameterizes a coupling matrix using random input and output modes and a specified spectrum. This model enables systematic study of the effects of low-dimensional structure in connectivity on neural activity. These effects manifest in features of collective activity, that we calculate, and can be undetectable when analyzing only single-neuron activities. We derive a relation between the effective rank of the coupling matrix and the dimension of activity. By extending the random-mode model, we compare the effects of single-neuron heterogeneity and low-dimensional connectivity. We also investigate the impact of structured overlaps between input and output modes, a feature of biological coupling matrices. Our theory provides tools to relate neural-network architecture and collective dynamics in artificial and biological systems., Comment: 35 pages, 11 figures

We consider $30^{\circ}$ twisted bilayer formed by two copies of Haldane model and explore evolution of its properties with varying interlayer coupling strength. Specifically, we compute the system's energy spectrum, its fractal dimensions, topological entanglement entropy, local Chern markers and anomalous Hall conductivity. We find that at weak interlayer coupling, the system remains gapped and retains topological properties of the isolated layers, but at strong interlayer coupling, the system forms a gapless multifractal state. We also establish that anomalous Hall conductivity can be used to characterize the system's topological properties in the same way as a local Chern marker., Comment: 10 pages, 9 figures

Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which uncovers sets of geometrically related nodes. {\em Geometric communities} consist of nodes ``closer'' to each other than to others in the graph. Some network features do not depend on node proximity -- rather, on them playing similar roles (e.g.\ building bridges) even if located far apart. These features can thus escape proximity-based analyses. We lack a general framework to uncover such features. We introduce {\em topological communities}, an alternative perspective to decomposing graphs. We find clusters that describe a network as much as classical communities, yet are missed by current techniques. In our framework, each graph guides our attention to its relevant features, whether geometric or topological. Our analysis complements existing ones, and could be a default method to study networks confronted without prior knowledge. Classical community detection has bolstered our understanding of biological, neural, or social systems; yet it is only half the story. Topological communities promise deep insights on a wealth of available data. We illustrate this for the global airport network, human connectomes, and others., Comment: 34 pages, 3 main figures, 22 supporting figures

We characterize the Many-Body Localization (MBL) phase transition using the dynamics of spread complexity and inverse participation ratio in the Krylov space starting from different initial states. Our analysis of the disordered Heisenberg spin-1/2 chain unravels that the ergodic-to-MBL transition can be determined from the transition of the pre-saturation peak in the thermofield double state (TFD) spread complexity. On the other hand, if an initially ordered state or a superposition of a small number of such states is chosen, then the saturation value of spread complexity and Krylov inverse participation ratio (KIPR) can distinguish the ergodic phase from the integrable phases, with no sharp difference between the integrable phases. Interestingly, the distinction between the disorder-free integrable and the MBL integrable phase is established by the spread complexity study of random states chosen from unitary and orthogonal Haar ensembles. We also study the complexity dynamics by coupling the system to a bath, which shows distinctive profiles in different phases. A stretched exponential decay of KIPR is observed when the MBL system is connected to the bath, with the decay starting at an earlier time for a greater value of environmental dephasing. Our work sheds light on the efficacy of Krylov space dynamics in understanding phase transitions in quantum many-body systems., Comment: 15 pages, 17 figures

Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical systems. Here we consider the physics of a charged quantum particle moving in a ``magnetic maze'': a high-dimensional space filled with a randomly chosen vector potential and a corresponding magnetic field. We derive a path integral description of the model by introducing appropriate collective variables and integrating out the random vector potential, and we solve for the dynamics in the limit of large dimensionality. We derive and analyze the equations of motion for Euclidean and real-time dynamics, and we calculate out-of-time-order correlators. We show that a special choice of vector potential correlations gives rise, in the low temperature limit, to a novel scale-invariant quantum theory with a tunable dynamical exponent. Moreover, we show that the theory is chaotic with a tunable chaos exponent which approaches the chaos bound at low temperature and strong coupling.

We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries that allows for the classification of similar and dissimilar pairs based on global correlations, and enables generalization from just a few samples. Unlike GQML algorithms developed to date, we propose to focus on symmetry-aware measurement adaptation that outperforms unitary parametrizations. We compare GQML for similarity testing against classical deep neural networks and convolutional neural networks with Siamese architectures. We show that quantum networks largely outperform their classical counterparts. We explain this difference in performance by analyzing correlated distributions used for composing our dataset. We relate the similarity testing with problems that showcase a proven maximal separation between the BQP complexity class and the polynomial hierarchy. While the ability to achieve advantage largely depends on how data are loaded, we discuss how similar problems can benefit from quantum machine learning., Comment: 5 pages, 5 figures

Using exact enumeration, the Casimir amplitude and the Casimir force are calculated for the square lattice Ising model with quenched surface disorder on one surface in cylinder geometry at criticality. The system shape is characterized by the aspect ratio $\rho=L/M$, where the cylinder length $L$ can take arbitrary values, while the circumference $M$ is varied from $M=4$ to $M=54$, resulting in up to $2^{54}$ numerically exact free energy calculations. A careful $M\to\infty$ extrapolation shows that quenched surface disorder is irrelevant in two dimensions, but gives rise to logarithmic corrections., Comment: 18 pages, 4 figures

We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method, we compute the spectral density of the equal-time covariance matrix characterizing the stationary states, demonstrating that this model undergoes a transition between stable and unstable states. In the stable regime, the spectral density has a finite and positive support, whereas negative eigenvalues emerge in the unstable regime. We determine the critical line separating these regimes and show that the spectral density exhibits a power-law tail at marginal stability, with an exponent independent of the temperature distribution. Additionally, we compute the spectral density of the lagged covariance matrix characterizing the stationary states of linear transformations of the original dynamical variables. Our random-matrix model is potentially interesting to understand the spectral properties of empirical correlation matrices appearing in the study of complex systems., Comment: 10 pages, 6 figures

We calculate the phase diagram of the Aubry-Andr\'{e} model as a function of filling and potential strength ($W$). We apply periodic boundary conditions and calculate the geometric Binder cumulant to determine the transition between the extended and localized phases. For rational fillings the phase transition occurs at $W=2t$ ($t$ denotes the hopping parameter), but spikes occur in the phase diagram at fillings which correspond to ratios of Fibonacci numbers. In the thermodynamic limit these ratios tend to specific irrational numbers, and $W \rightarrow 0$ at these fillings. We also calculate the phase diagram of an extended Aubry-Andr\'{e} model with second nearest neighbor hoppings. In addition to spikes, this phase diagram also exhibits discontinuities (jumps) at some of the irrational fillings at which the spikes occur.

We study percolation problems of overlapping objects where the underlying geometry is such that in D-dimensions, a subset of the directions has a lattice structure, while the remaining directions have a continuum structure. The resulting semicontinuum problem describes the percolation of overlapping shapes in parallel layers or lanes with positional constraints for the placement of the objects along the discrete directions. Several semicontinuum percolation systems are analyzed like hypercuboids with a particular focus on 2D and 3D cases, disks, and parallelograms. Adapting the excluded volume arguments to the semicontinuum setting, we show that for the semicontinuum problem of hypercuboids, for fixed side-lengths of the hypercuboids along the directions in which a lattice structure is maintained, the percolation threshold is always independent of the side-lengths along the continuum directions. The result holds even when there is a distribution for the side-lengths along the continuum directions. Trends in the variation of the thresholds, as we vary the linear measure of the shapes along the continuum directions, are obtained for other semicontinuum models like disks and parallelograms in 2D. The results are compared with those of corresponding continuum and lattice models. For the 2D and 3D models considered, using Monte Carlo simulations, we verify the excluded volume predictions for the trends and numerical values of the percolation thresholds. Very good agreement is seen between the predicted numerical values and the simulation results. The semicontinuum setting also allows us to establish a connection between the percolation problem of overlapping shapes in 2D continuum and triangular lattice. We also verify that the isotropy of the threshold for anisotropic shapes and standard percolation universality class is maintained in the semicontinuum setting., Comment: 13 pages, 11 figures, 7 tables

Perceptions and actions, thoughts and memories result from coordinated activity in hundreds or even thousands of neurons in the brain. It is an old dream of the physics community to provide a statistical mechanics description for these and other emergent phenomena of life. These aspirations appear in a new light because of developments in our ability to measure the electrical activity of the brain, sampling thousands of individual neurons simultaneously over hours or days. We review the progress that has been made in bringing theory and experiment together, focusing on maximum entropy methods and a phenomenological renormalization group. These approaches have uncovered new, quantitatively reproducible collective behaviors in networks of real neurons, and provide examples of rich parameter--free predictions that agree in detail with experiment.

Disordered systems generically exhibit aging and a glass transition. Previous studies have long suggested that non-reciprocity tends to destroy glassiness. Here, we show that this is not always the case using a bipartite spherical Sherrington-Kirpatrick model that describes the antagonistic coupling between two identical complex agents modeled as macroscopic spin glasses. Our dynamical mean field theory calculations reveal an exceptional-point mediated transition from a static disorder phase to an oscillating amorphous phase as well as non-reciprocal aging with slow dynamics and oscillations., Comment: 18 pages, 13 figures

We apply a state-of-the-art difference-in-differences approach to estimate the impact of ChatGPT's release on the writing style of condensed matter papers on arXiv. Our analysis reveals a statistically significant improvement in the English quality of abstracts written by non-native English speakers. Importantly, this improvement remains robust even after accounting for other potential factors, confirming that it can be attributed to the release of ChatGPT. This indicates widespread adoption of the tool. Following the release of ChatGPT, there is a significant increase in the use of unique words, while the frequency of rare words decreases. Across language families, the changes in writing style are significant for authors from the Latin and Ural-Altaic groups, but not for those from the Germanic or other Indo-European groups., Comment: 9 pages, 1 figure, 7 tables

Quantum-mechanics-based transport simulation is of importance for the design of ultra-short channel field-effect transistors (FETs) with its capability of understanding the physical mechanism, while facing the primary challenge of the high computational intensity. Traditional machine learning is expected to accelerate the optimization of FET design, yet its application in this field is limited by the lack of both high-fidelity datasets and the integration of physical knowledge. Here, we introduced a physics-integrated neural network framework to predict the transport curves of sub-5-nm gate-all-around (GAA) FETs using an in-house developed high-fidelity database. The transport curves in the database are collected from literature and our first-principles calculations. Beyond silicon, we included indium arsenide, indium phosphide, and selenium nanowires with different structural phases as the FET channel materials. Then, we built a physical-knowledge-integrated hyper vector neural network (PHVNN), in which five new physical features were added into the inputs for prediction transport characteristics, achieving a sufficiently low mean absolute error of 0.39. In particular, ~98% of the current prediction residuals are within one order of magnitude. Using PHVNN, we efficiently screened out the symmetric p-type GAA FETs that possess the same figures of merit with the n-type ones, which are crucial for the fabrication of homogeneous CMOS circuits. Finally, our automatic differentiation analysis provides interpretable insights into the PHVNN, which highlights the important contributions of our new input parameters and improves the reliability of PHVNN. Our approach provides an effective method for rapidly screening appropriate GAA FETs with the prospect of accelerating the design process of next-generation electronic devices., Comment: 13 pages, 4 figures

Competition between magnetism and superconductivity can lead to unconventional and topological superconductivity. However, the experimental confirmation of the presence of Majorana edge states and unconventional pairing currently poses a major challenge. Here we consider a two-dimensional lattice model for a superconductor with spin-orbit coupling and exchange coupling to randomly distributed magnetic impurities. Depending on parameters of the model, this system may display topologically trivial or nontrivial edge states. We map out the phase diagram by computing the Bott index, a topological invariant defined in real space. We then use machine learning (ML) algorithms to predict the Bott index from the local density of states (LDOS) at zero energy, obtaining high-accuracy results. We also train ML models to predict the amplitude of odd-frequency pairing in the anomalous Green's function at zero energy. Once the ML models are trained using the LDOS, which is experimentally accessible via scanning tunneling spectroscopy, our method could be applied to predict the number of Majorana edge states and to estimate the magnitude of odd-frequency pairing in real materials., Comment: 10 pages, 8 figures

Finding optimal wave sampling methods has far-reaching implications in wave physics, such as seismology, acoustics, and telecommunications. A key challenge is surpassing the Whittaker-Nyquist-Shannon (WNS) aliasing limit, establishing a frequency below which the signal cannot be faithfully reconstructed. However, the WNS limit applies only to periodic sampling, opening the door to bypass aliasing by aperiodic sampling. In this work, we investigate the efficiency of a recently discovered family of aperiodic monotile tilings, the Hat family, in overcoming the aliasing limit when spatially sampling a wavefield. By analyzing their spectral properties, we show that monotile aperiodic seismic (MAS) arrays, based on a subset of the Hat tiling family, are efficient in surpassing the WNS sampling limit. Our investigation leads us to propose MAS arrays as a novel design principle for seismic arrays. We show that MAS arrays can outperform regular and other aperiodic arrays in realistic beamforming scenarios using single and distributed sources, including station-position noise. While current seismic arrays optimize beamforming or imaging applications using spiral or regular arrays, MAS arrays can accommodate both, as they share properties with both periodic and aperiodic arrays. More generally, our work suggests that aperiodic monotiles can be an efficient design principle in various fields requiring wave sampling., Comment: 18 pages, 10 figures

Coherent information quantifies the transmittable quantum information through a channel and is directly linked to the channel's quantum capacity. In the context of dynamical purification transitions, scrambling dynamics sustain extensive and positive coherent information at low measurement rates, but noises can suppress it to zero or negative values. Here we introduce quantum-enhanced operations into a noisy monitored quantum circuit. This circuit, viewed as a quantum channel, undergoes a phase transition in coherent information from a recoverable phase with positive values to an irrecoverable phase with negative values. This transition is modulated by the relative frequency of noise and quantum-enhanced operations. The existence of a recoverable phase implies that quantum-enhanced operations can facilitate reliable quantum information transmission in the presence of diverse noises. Remarkably, we propose a resource-efficient protocol to characterize this phase transition, effectively avoiding post-selection by utilizing every run of the quantum simulation. This approach bridges the gap between theoretical insights and practical implementation, making the phase transition feasible to demonstrate on realistic noisy intermediate-scale quantum devices.

An elastic spring network is an example of evolvable matter. It can be pruned to couple separated pairs of nodes so that when a strain is applied to one of them, the other responds either in-phase or out-of-phase. This produces two pruned networks with incompatible functions that are nearly identical but differ from each other by a set of "mutations," each of which removes or adds a single bond in the network. The effect of multiple mutations is epistatic; that is, the effect of a mutation depends on what other mutations have already occurred. We generate ensembles of network pairs that differ by a fixed number, $M$, of discrete mutations and evaluate all $M!$ mutational paths between the in- and out-of phase behaviors up to $M = 14$. With a threshold response for the network to be considered functional, so that non-functional networks are disallowed, only some mutational pathways are viable. We find that there is a surprisingly high critical response threshold above which no evolutionarily viable path exists between the two networks. The few remaining pathways at this critical value dictate much of the behavior along the evolutionary trajectory. In most cases, the mutations break up into two distinct classes. The analysis clarifies how the number of mutations and the position of a mutation along the pathway affect the evolutionary outcome.

We study the finite size scaling of the bulk polarization in a quasiperiodic (Aubry-Andr\'{e}) model using the geometric analog of the Binder cumulant. As a proof of concept we show that the geometric Binder cumulant method described here can reproduce the known literature values for the flat and raised cosine distributions, which are the two distributions that occur in the delocalized phase. For the Aubry-Andr\'{e} model at half-filling the phase transition point is accurately reproduced. Not only is the correct size scaling exponent of the variance obtained in the extended and the localized phases, but the geometric Binder cumulant undergoes a sign change at the phase transition. We also calculate the state resolved Binder cumulant as a function of disorder strength to gain insight into the mechanism of the localization transition.

Temperature chaos (TC) in spin glasses has been claimed to exist no matter how small the temperature change, $\Delta T$. However, experimental studies exhibit a finite value of $\Delta T$ for the transition to TC. This paper explores the onset of TC with much higher accuracy over a large temperature range. We find that TC is always present, though small for the smallest $\Delta T$ that we can reliably measure. However, it grows rapidly as $\Delta T$ increases, the region of rapid growth coinciding with the $\Delta T$ predicted from renormalization group arguments and observed experimentally. We are able to transcend the full range for the onset of TC, from fully reversible to fully chaotic.

Variable selection is a problem of statistics that aims to find the subset of the $N$-dimensional possible explanatory variables that are truly related to the generation process of the response variable. In high-dimensional setups, where the input dimension $N$ is comparable to the data size $M$, it is difficult to use classic methods based on $p$-values. Therefore, methods based on the ensemble learning are often used. In this review article, we introduce how the performance of these ensemble-based methods can be systematically analyzed using the replica method from statistical mechanics when $N$ and $M$ diverge at the same rate as $N,M\to\infty, M/N\to\alpha\in(0,\infty)$. As a concrete application, we analyze the power of stability selection (SS) and the derandomized knockoff (dKO) with the $\ell_1$-regularized statistics in the high-dimensional linear model. The result indicates that dKO provably outperforms the vanilla knockoff and the standard SS, while increasing the bootstrap resampling rate in SS might further improve the detection power., Comment: 25 pages, 4 figures, 1 table

In geometrically frustrated (GF) magnets, conventional long-range order is suppressed due to the presence of primitive triangular structural units, and the nature of the ensuing ground state remains elusive. One class of candidate states, extensively sought in experiments and vigorously studied theoretically, is the quantum spin liquid (QSL), a magnetically-disordered state in which all spins participate in a quantum-coherent many-body state. Randomly located impurities, present in all materials, may prevent QSL formation and instead lead to the formation of a spin-glass state. In this article, we review available data on the specific heat, magnetic susceptibility, and neutron scattering in GF materials. Such data show that a pure GF magnet possesses a characteristic ``hidden energy scale'' significantly exceeded by the other microscopic energy scales in the material. When cooled down to a temperature below the hidden energy scale, a GF material develops significant short-range order that dominates its properties and, in particular, dictates the spin-glass transition temperature for experimentally accessible impurity densities. We review the manifestations of short-range order in the commonly observed thermodynamics quantities in GF materials, possible scenarios for the hidden energy scale, and related open questions., Comment: 41 pages, 5 figures

A different type of topological phase dubbed topological inverse Anderson insulators is proposed, which is characterized by the disorder-induced extended bulk states from the flat-band localization and topological edge states. Based on the topological invariant, the behaviors of the localization length of the zero-energy modes, and quantum transport, we identify its existence in several all-band-flat models with the disordered potentials or hopping including the $\pi$-flux Creutz ladder, the fully dimerized Su-Schrieffer-Heeger chain, and $\pi$-flux diamond chain. Unlike the topological Anderson insulator, where disorder induces localization and exponential suppression of transport, the disorder-assisted quantum ballistic coherent transport can appear in the topological inverse Anderson insulator. In addition, our proposal and results could be realized by the current experimental techniques., Comment: 9 pages, 5 figures

Autoregressive models are a class of generative model that probabilistically predict the next output of a sequence based on previous inputs. The autoregressive sequence is by definition one-dimensional (1D), which is natural for language tasks and hence an important component of modern architectures like recurrent neural networks (RNNs) and transformers. However, when language models are used to predict outputs on physical systems that are not intrinsically 1D, the question arises of which choice of autoregressive sequence -- if any -- is optimal. In this paper, we study the reconstruction of critical correlations in the two-dimensional (2D) Ising model, using RNNs and transformers trained on binary spin data obtained near the thermal phase transition. We compare the training performance for a number of different 1D autoregressive sequences imposed on finite-size 2D lattices. We find that paths with long 1D segments are more efficient at training the autoregressive models compared to space-filling curves that better preserve the 2D locality. Our results illustrate the potential importance in choosing the optimal autoregressive sequence ordering when training modern language models for tasks in physics., Comment: 12 pages, 4 figures

The study of structure-spectrum relationships is essential for spectral interpretation, impacting structural elucidation and material design. Predicting spectra from molecular structures is challenging due to their complex relationships. Herein, we introduce NMRNet, a deep learning framework using the SE(3) Transformer for atomic environment modeling, following a pre-training and fine-tuning paradigm. To support the evaluation of NMR chemical shift prediction models, we have established a comprehensive benchmark based on previous research and databases, covering diverse chemical systems. Applying NMRNet to these benchmark datasets, we achieve state-of-the-art performance in both liquid-state and solid-state NMR datasets, demonstrating its robustness and practical utility in real-world scenarios. This marks the first integration of solid and liquid state NMR within a unified model architecture, highlighting the need for domainspecific handling of different atomic environments. Our work sets a new standard for NMR prediction, advancing deep learning applications in analytical and structural chemistry., Comment: 23 pages, 6 figures

``Deep thermalization'' describes the emergence of universal wavefunction distributions in quantum many-body dynamics, appearing on a local subsystem upon measurement of its environment. In this work, we study in detail the effect of continuous internal symmetries and associated conservation laws on deep thermalization. Concretely, we consider quantum spin systems with a $U(1)$ symmetry associated with the conservation of magnetization (or `charge'), and analyze how the choice of initial states (specifically, their degree of charge fluctuations) and the choice of measurement basis (specifically, whether or not it can reveal information about the local charge density) determine the ensuing universal wavefunction distributions. We find a rich set of possibilities. First we focus on the case of a random state of well-defined charge subjected to charge-revealing masurements, and rigorously prove that the projected ensemble approaches a direct sum of Haar ensembles in the charge sectors of the subsystem of interest. We then analytically derive the limiting wavefunction distributions for more general initial states and measurement bases, finding results that include the Haar ensemble, the ``Scrooge ensemble'' (a distortion of the Haar ensemble by a density matrix), and the ``generalized Scrooge ensemble'' (a stochastic mixture of multiple Scrooge ensembles). These represent nontrivial higher-moment generalizations of the Gibbs state, and notably can depend on the entire charge distribution of the initial state, not just its average. Our findings demonstrate a rich interplay between symmetries and the information extracted by measurements, which allows deep thermalization to exhibit a range of universal behaviors far beyond regular thermalization., Comment: 15+15 pages, 8+3 figures

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformer architectures can implement the optimal Belief Propagation algorithm on both root classification and masked language modeling tasks. Correlations at larger distances corresponding to increasing layers of the hierarchy are sequentially included as the network is trained. We analyze how the transformer layers succeed by focusing on attention maps from models trained with varying degrees of filtering. These attention maps show clear evidence for iterative hierarchical reconstruction of correlations, and we can relate these observations to a plausible implementation of the exact inference algorithm for the network sizes considered., Comment: 18 pages, 9 figures