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The properties of a two-dimensional electron gas (2DEG) in a semiconductor host with two valleys related by an underlying $C_4$ rotational symmetry are studied using Hartree-Fock (HF) and various other many-body approaches. A familiar artifact of the HF approach is a degeneracy between the valley polarized - ``Ising nematic'' - and spin polarized - ferromagnetic - phases, which is inconsistent with recent variational Monte Carlo (VMC) results. Correlation effects, computed either within the random phase approximation (RPA) or the T-matrix approximation, enhance the valley susceptibility relative to the spin susceptibility. Extrapolating the results to finite interaction strength, we find a direct first-order transition from a symmetry-unbroken state to a spin unpolarized Ising nematic fluid with full valley polarization, in qualitative agreement with VMC. The RPA results are also reminiscent of experiments on the corresponding 2DEG in AlAs heterostructures., Comment: 6 + 25 pages, 12 figures

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from NRG.Due to the overcompleteness, we achieve only qualitative agreement., Comment: 9 pages, 4 figures

While current research and development of autonomous driving primarily focuses on developing new features and algorithms, the transfer from isolated software components into an entire software stack has been covered sparsely. Besides that, due to the complexity of autonomous software stacks and public road traffic, the optimal validation of entire stacks is an open research problem. Our paper targets these two aspects. We present our autonomous research vehicle EDGAR and its digital twin, a detailed virtual duplication of the vehicle. While the vehicle's setup is closely related to the state of the art, its virtual duplication is a valuable contribution as it is crucial for a consistent validation process from simulation to real-world tests. In addition, different development teams can work with the same model, making integration and testing of the software stacks much easier, significantly accelerating the development process. The real and virtual vehicles are embedded in a comprehensive development environment, which is also introduced. All parameters of the digital twin are provided open-source at https://github.com/TUMFTM/edgar_digital_twin.

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with $C_4$ (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground-state. Our results are of direct relevance to the recently discovered ``nematic'' state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, $m_x/m_y\approx 5.2$, we obtain a transition from an anisotropic metal to a valley-polarized metal at $r_s \approx 12$ (where $r_s$ is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy., Comment: 5+20 pages

The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on inhomogeneous graphs. However, the irregularity of the graph structure and the vastness of configurational spaces present a fundamental challenge to theoretical tools, such as the renormalization group, which were so successful in characterizing the universal physical behaviour in critical phenomena. Here we show that compression theory allows to extract relevant degrees of freedom in arbitrary geometries, and develop efficient numerical tools to build an effective theory from data. We demonstrate our method by applying it to a strongly interacting system on an Ammann-Beenker quasicrystal, where it discovers an exotic critical point with broken conformal symmetry., Comment: 9 pages, 7 figures

Engineering long-range interacting spin systems with ultra cold atoms offers the possibility to explore exotic magnetically ordered phases in strongly-correlated scenarios. Quantum gases in optical cavities provide a versatile experimental platform to further engineer photon-mediated interactions and access the underlying microscopic processes by probing the cavity field. Here, we study a two-component spin Bose-Hubbard system with cavity-mediated interactions. We provide a comprehensive overview of its phase diagram and transitions in experimentally relevant regimes. The interplay of different energy scales yields a rich phase diagram with superfluid and insulating phases exhibiting density modulation or spin ordering. In particular, the combined effect of contact and global-range interactions gives rise to an antiferromagnetically ordered phase for arbitrarily small spin-dependent light-matter coupling, while long-range and inter-spin contact interactions introduce regions of instability and phase separation in the phase diagram. We further study the low energy excitations above the antiferrogmagnetic phase. Besides particle-hole branches, it hosts spin-exchange excitations with a tunable energy gap. The studied lattice model can be readily realized in cold-atom experiments with optical cavities., Comment: 8(+10) pages, 4(+7) figures

The vanguard of many-body theory is nowadays dealing with the full frequency dynamics of n-point Green's functions for n higher than two. Numerically, these objects easily become a memory bottleneck, even when working with discrete imaginary-time Matsubara frequencies. Here, we use the intermediate representation (IR) to compactify the two-point Green's function and three-point Fermion-Bose vertex directly on the real frequency axis, on the basis of numerical renormalization group (NRG) data. We empirically observe an upper bound of the relative error when comparing the IR reconstructed signal with the original NRG data, and demonstrate that a IR compacification is possible., Comment: 15 pages, 12 figures

Mitigating the energy requirements of artificial intelligence requires novel physical substrates for computation. Phononic metamaterials have a vanishingly low power dissipation and hence are a prime candidate for green, always-on computers. However, their use in machine learning applications has not been explored due to the complexity of their design process: Current phononic metamaterials are restricted to simple geometries (e.g. periodic, tapered), and hence do not possess sufficient expressivity to encode machine learning tasks. We design and fabricate a non-periodic phononic metamaterial, directly from data samples, that can distinguish between pairs of spoken words in the presence of a simple readout nonlinearity; hence demonstrating that phononic metamaterials are a viable avenue towards zero-power smart devices., Comment: 13 pages, 11 figures

Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms - even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean-field. Hence, a nonzero superfluid weight constitutes a nontrivial bulk property that distinguishes obstructed bands from trivial bands in the presence of interactions., Comment: 5+31 pages, 3+2 figures, 2 tables

Real-space mutual information (RSMI) was shown to be an important quantity, formally and from a numerical standpoint, in finding coarse-grained descriptions of physical systems. It very generally quantifies spatial correlations, and can give rise to constructive algorithms extracting relevant degrees of freedom. Efficient and reliable estimation or maximization of RSMI is, however, numerically challenging. A recent breakthrough in theoretical machine learning has been the introduction of variational lower bounds for mutual information, parametrized by neural networks. Here we describe in detail how these results can be combined with differentiable coarse-graining operations to develop a single unsupervised neural-network based algorithm, the RSMI-NE, efficiently extracting the relevant degrees of freedom in the form of the operators of effective field theories, directly from real-space configurations. We study the information contained in the statistical ensemble of constructed coarse-graining transformations, and its recovery from partial input data using a secondary machine learning analysis applied to this ensemble. In particular, we show how symmetries, also emergent, can be identified. We demonstrate the extraction of the phase diagram and the order parameters for equilibrium systems, and consider also an example of a non-equilibrium problem., Comment: Accepted version. Added new discussion of symmetries in the ensemble of coarse-graining rules. 27 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:2101.11633

Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated. Thus, an efficient parametrization of the wave-function can become challenging. In this letter we introduce a neural-network based variational ansatz that retains the flexibility of these generic methods while allowing for a tunability with respect to the relevant correlations governing the physics of the system. We illustrate the success of this approach on topological, long-range correlated and frustrated models. Additionally, we introduce compatible variational optimization methods for exploration of low-lying excited states without symmetries that preserve the interpretability of the ansatz., Comment: 14 pages, 18 figures, code available at https://github.com/cmt-qo/cm-cRBM

Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking of large scale dynamical quantum systems represents a major challenge due to lack of efficient tools for their simulation. Here, we present a scalable algorithm based on neural networks for Hamiltonian tomography in out-of-equilibrium quantum systems. We illustrate our approach using a model for a forefront quantum simulation platform: ultracold atoms in optical lattices. Specifically, we show that our algorithm is able to reconstruct the Hamiltonian of an arbitrary size quasi-1D bosonic system using an accessible amount of experimental measurements. We are able to significantly increase the previously known parameter precision., Comment: 13 pages, 13 figures, code: https://gitlab.com/QMAI/papers/manybodydynlearning

Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building., Comment: Version accepted for publication in Physical Review Letters. See also the companion manuscript arXiv:2103.16887 "Symmetries and phase diagrams with real-space mutual estimation neural estimation"

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a non-zero Chern number or fragile topology sets a lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we use numerically exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. We then investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity., Comment: 5 pages, 3 figures + supplemental material (14 pages, 4 figures)

Weyl semimetals in a magnetic field give rise to interesting non-local electronic orbits: the ballistic transport through the bulk enabled by the chiral Landau levels is combined with a momentum-space sliding along the surface Fermi-arc driven by the Lorentz force. Bulk chiral Landau levels can also be induced by axial fields whose sign depends on the chirality of the Weyl point. However, the microscopic perturbations that give rise to them can be described in terms of gauge fields only in the low-energy sectors around the Weyl points. In addition, since pseudo-fields are intrinsic, there is no apparent reason for a Lorentz force that causes sliding along the Fermi-arcs. Therefore, the existence of non-local orbits driven exclusively by pseudo-fields is not obvious. Here, we show that for systems with at least four Weyl points in the bulk spectrum, non-local orbits can be induced by axial fields alone. We discuss the underlying mechanisms by a combination of analytical semi-classical theory, the microscopic numerical study of wave-packet dynamics, and a surface Green's function analysis., Comment: 12 pages, 5 figures

We derive generalized Kronig identities expressing quadratic fermionic terms including momentum transfer to bosonic operators and use them to obtain the exact solution for one-dimensional fermionic models with linear dispersion in the presence of position-dependent interactions and scattering potential. In these Luttinger droplets, which correspond to Luttinger liquids with spatial variations or constraints, the position dependences of the couplings break the translational invariance of correlation functions and modify the Luttinger-liquid interrelations between excitation velocities., Comment: 14 pages, 2 figures

Thin nanomaterials are key constituents of modern quantum technologies and materials research. Identifying specimens of these materials with properties required for the development of state of the art quantum devices is usually a complex and lengthy human task. In this work we provide a neural-network driven solution that allows for accurate and efficient scanning, data-processing and sample identification of experimentally relevant two-dimensional materials. We show how to approach classification of imperfect imbalanced data sets using an iterative application of multiple noisy neural networks. We embed the trained classifier into a comprehensive solution for end-to-end automatized data processing and sample identification., Comment: 8 pages, 4 figures

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior theoretical knowledge. While for phases characterized by a broken symmetry, the use of unsupervised methods has proven to be successful, topological phases without a local order parameter seem to be much harder to identify without supervision. Here, we use an unsupervised approach to identify topological phases and transitions out of them. We train artificial neural nets to relate configurational data or measurement outcomes to quantities like temperature or tuning parameters in the Hamiltonian. The accuracy of these predictive models can then serve as an indicator for phase transitions. We successfully illustrate this approach on both the classical Ising gauge theory as well as on the quantum ground state of a generalized toric code., Comment: 12 pages, 13 figures

Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. The integer quantum Hall effect has delivered on that promise in the electronic realm through high-precision metrology devices. However, both the route of implementing an analogue of the quantum Hall effect as well as the quantum spin Hall effect are obstructed for acoustics by the requirement of a magnetic field, or the presence of fermionic quantum statistics, respectively. Here, we use a two-dimensional acoustic crystal with two layers to mimic spin-orbit coupling, a crucial ingredient of topological insulators. In particular, our setup allows us to free ourselves of symmetry constraints as we rely on the concept of a non-vanishing "spin" Chern number. We experimentally characterize the emerging boundary states which we show to be gapless and helical. Moreover, in an H-shaped device we demonstrate how the transport path can be selected by tuning the geometry, enabling the construction of complex networks.

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: while answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions., Comment: 4 pages, 3 figures + supplementary information (21 pages, 13 figures, 7 tables). Note the accompanying paper by Zhi-Da Song et al. "Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology"' posted on the same day on the arXiv

The efficient validation of quantum devices is critical for emerging technological applications. In a wide class of use-cases the precise engineering of a Hamiltonian is required both for the implementation of gate-based quantum information processing as well as for reliable quantum memories. Inferring the experimentally realized Hamiltonian through a scalable number of measurements constitutes the challenging task of Hamiltonian learning. In particular, assessing the quality of the implementation of topological codes is essential for quantum error correction. Here, we introduce a neural net based approach to this challenge. We capitalize on a family of exactly solvable models to train our algorithm and generalize to a broad class of experimentally relevant sources of errors. We discuss how our algorithm scales with system size and analyze its resilience towards various noise sources., Comment: 15 pages, 12 figures. Code available at https://github.com/cmt-qo/cm-toricCode

Three dimensional Weyl semimetals exhibit open Fermi arcs on their sample surfaces connecting the projection of bulk Weyl points of opposite chirality. The canonical interpretation of these surfaces states is in terms of chiral edge modes of a layer quantum Hall effect: The two-dimensional momentum-space planes perpendicular to the momentum connecting the two Weyl points are characterized by a non-zero Chern number. It might be interesting to note, that in analogy to the known two-dimensional Floquet anomalous chiral edge states, one can realize open Fermi arcs in the absence of Chern numbers in periodically driven system. Here, we present a way to construct such anomalous Fermi arcs in a concrete model.

The non-trivial geometry encoded in the Quantum Mechanical wavefunctions has important consequences for its single-particle as well as many-body dynamics. Yet, our understanding of how the geometry of the single-particle eigenstates are manifest in the characteristics of a many-particle system is still incomplete. Here, we demonstrate how the single-particle Berry curvature modifies the fluxoid quantization of a two dimensional Bardeen-Cooper-Schrieffer (BCS) superconductor, and discuss the experimental scenarios where this anomalous quantization is expected to be realized., Comment: 5 pages, 2 figures, Comments welcome

Recently a novel real-space RG algorithm was introduced, identifying the relevant degrees of freedom of a system by maximizing an information-theoretic quantity, the real-space mutual information (RSMI), with machine learning methods. Motivated by this, we investigate the information theoretic properties of coarse-graining procedures, for both translationally invariant and disordered systems. We prove that a perfect RSMI coarse-graining does not increase the range of interactions in the renormalized Hamiltonian, and, for disordered systems, suppresses generation of correlations in the renormalized disorder distribution, being in this sense optimal. We empirically verify decay of those measures of complexity, as a function of information retained by the RG, on the examples of arbitrary coarse-grainings of the clean and random Ising chain. The results establish a direct and quantifiable connection between properties of RG viewed as a compression scheme, and those of physical objects i.e. Hamiltonians and disorder distributions. We also study the effect of constraints on the number and type of coarse-grained degrees of freedom on a generic RG procedure., Comment: Updated manuscript with new results on disordered systems

Experiments with quantum gas microscopes have started to explore the antiferromagnetic phase of the two-dimensional Fermi-Hubbard model and effects of doping with holes away from half filling. In this work we show how direct measurements of the system averaged two-spin density matrix and its full counting statistics can be used to identify different correlated magnetic phases with or without long-range order. We discuss examples of phases which are potentially realized in the Hubbard model close to half filling, including antiferrromagnetically ordered insulators and metals, as well as insulating spin-liquids and metals with topological order. For these candidate states we predict the doping- and temperature dependence of local correlators, which can be directly measured in current experiments., Comment: 15 pages, 7 figures

Condensed-matter and other engineered systems, such as cold atoms, photonic, or phononic metamaterials, have proven to be versatile platforms for the observation of low-energy counterparts of elementary particles from relativistic field theories. These include the celebrated Majorana modes, as well as Dirac and Weyl fermions. An intriguing feature of the Weyl equation is the chiral symmetry, where the two chiral sectors have an independent gauge freedom. While this freedom leads to a quantum anomaly, there is no corresponding axial background field coupling differently to opposite chiralities in quantum electrodynamics. Here, we provide the experimental characterization of the effect of such an axial field in an acoustic metamaterial. We implement the axial field through an inhomogeneous potential and observe the induced chiral Landau levels. From the metamaterials perspective these chiral channels open the possibility for the observation of non-local Weyl orbits and might enable unidirectional bulk transport in a time-reversal invariant system.

High-order topological insulators are a recent development extending the topological theory of charge polarization to higher multipole moments. Since their theoretical proposal, several experimental realizations of high-order topological insulators have been reported. However, high order topological transitions have not been observed. In this letter, we report on the observation of a high-order topological transition in a quadrupole topological insulator implemented in an LC circuit with nonlinear couplings. This system presents the ability to confine electromagnetic energy in its corner states, with a localization length that can be tuned over a broad range through the use of an external bias voltage. Additionally, we provide an experimental characterization and an effective theory for the boundary states, further corroborating their topological nature by direct measurement of the winding number.

In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground state energy of lattice models with completely flat band structure in a ring geometry. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum $\Phi_0/2 = hc/(2e)$ period, indicating that only bound pairs of particles with charge $2e$ are propagating, while single quasiparticles with charge $e$ remain localized. We show analytically in one dimension that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover we construct an extensive number of exact conserved quantities for the one dimensional lattice models. These conserved quantities are associated to the occupation of localized single quasiparticle states. Our results imply that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state., Comment: 24 pages, 10 figures. This version version is almost identical to the published one. Some minor errors present in the published version have been corrected here

Coherently splitting a one-dimensional Bose gas provides an attractive, experimentally estab- lished platform to investigate many-body quantum dynamics. At short enough times, the dynamics is dominated by the dephasing of single quasi-particles, and well described by the relaxation to- wards a generalized Gibbs ensemble corresponding to the free Luttinger theory. At later times on the other hand, the approach to a thermal Gibbs ensemble is expected for a generic, interacting quantum system. Here, we go one step beyond the quadratic Luttinger theory and include the lead- ing phonon-phonon interactions. By applying kinetic theory and non-equilibrium Dyson-Schwinger equations, we analyze the full relaxation dynamics beyond dephasing and determine the asymptotic thermalization process in the two-wire system for a symmetric splitting protocol. The major ob- servables are the different phonon occupation functions and the experimentally accessible coherence factor, as well as the phase correlations between the two wires. We demonstrate that, depending on the splitting protocol, the presence of phonon collisions can have significant influence on the asymptotic evolution of these observables, which makes the corresponding thermalization dynamics experimentally accessible., Comment: 21 pages, 12 figures

We present an exact ground state solution of a quantum dimer model introduced in Ref.[1], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-$T_c$ cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit., Comment: Revised version, 8 pages

Phononic crystals and metamaterials take advantage of pre-designed geometrical structures to sculpt elastic waves, controlling their dispersion using different mechanisms. These mechanisms revolve mostly around Bragg scattering (BS), local resonances (LR) and inertial amplification (IA), which employ ad-hoc, often problem-specific geometries. Here, we use parametrized, spiraling unit cells as building blocks for designing various types of phononic materials. We focus on planar spirals that are easy to fabricate, yet give rise to the desirable complex dynamics. By simple modifications of the spirals, we open full band gaps using BS, LR and IA. Moreover, we alter the underlying unit cell symmetry and lattice vectors, to create wave beaming and topologically protected band gaps, both affecting waves whose wavelength is much larger than the order of periodicity.

We study single electron spectral functions in a quantum dimer model introduced by Punk, Allais and Sachdev (Ref. [1]). The Hilbert space of this model is spanned by hard-core coverings of the square lattice with two types of dimers: ordinary bosonic spin-singlets, as well as fermionic dimers carrying charge +e and spin 1/2, which can be viewed as bound-states of spinons and holons in a doped resonating valence bond (RVB) liquid. This model realizes a metallic phase with topological order and captures several properties of the pseudogap phase in hole-doped cuprates, such as a reconstructed Fermi surface with small hole-pockets and a highly anisotropic quasiparticle residue in the absence of any broken symmetries. Using a combination of exact diagonalization and analytical methods we compute electron spectral functions and show that this model indeed exhibits a sizeable antinodal pseudogap, with a momentum dependence deviating from a simple d-wave form, in accordance with experiments on underdoped cuprates., Comment: 13 pages, 7 figures

The modern theory of charge polarization in solids is based on a generalization of Berry's phase. Its possible quantization lies at the heart of our understanding of all systems with topological band structures that were discovered over the last decades. While based on the concept of the "charge" polarization, the same theory can be used as an elegant tool to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. Recently, the theory of this quantized polarization was extended from the dipole- to higher multipole-moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge-modes, which in turn stabilize zero-dimensional in-gap corner states. However, such a state of matter has not been observed experimentally. Here, we provide the first measurements of a phononic quadrupole insulator. We experimentally characterize the bulk, edge, and corner physics of a mechanical metamaterial and find the predicted gapped edge and in-gap corner states. We further corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases predicted by the quadrupole theory. From an application point of view, these topological corner states are an important stepping stone on the way to topologically protected wave-guides in higher dimensions and thereby open a new design path for metamaterials., Comment: Submitted to journal on July 15, 2017

The ability to design and fabricate materials with tailored mechanical properties, combined with immunity to damage, is a frontier of materials engineering. For example, materials which are characterized by elastic properties that depend on the position inside a medium are required in applications where structural stability has to be combined with a soft and compliant surface, like in impact protection and cushioning. A gradient in the elastic properties can be built from a single material, varying gradually the bulk porosity of the material or its geometrical structure. However, if such a gradient is built into the material at production, damage or wearing over time might expose unwanted elastic properties. Here, we implement a design principle for a spatially inhomogeneous material based on topological band-theory for mechanical systems. The resulting inhomogeneity is stable against wearing and even cutting the material in half. We show how, by creating a periodic elastic material with topological properties, one can create an intrinsically polar behavior, where a face with a given surface normal is stiff while its opposing face is soft.

We show that a transition metal dichalcogenide monolayer with a radiatively broadened exciton resonance would exhibit perfect extinction of a transmitted field. This result holds for s- or p-polarized weak resonant light fields at any incidence angle, due to the conservation of in-plane momentum of excitons and photons in a flat defect-free two dimensional crystal. In contrast to extinction experiments with single quantum emitters, exciton-exciton interactions lead to an enhancement of reflection with increasing power for incident fields that are blue detuned with respect to the exciton resonance. We show that the interactions limit the maximum reflection that can be achieved by depleting the incoming coherent state into an outgoing two-mode squeezed state., Comment: Comments welcome

Discrete models provide concise descriptions of complex physical phenomena, such as negative refraction, topological insulators, and Anderson localization. While there are multiple tools to obtain discrete models that demonstrate particular phenomena, it remains a challenge to find metamaterial designs that replicate the behavior of desired nontrivial discrete models. Here we solve this problem by introducing a new class of metamaterial, which we term 'perturbative metamaterial', consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model (individual masses and springs) to individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing 2D mechanical metamaterials that realize Veselago lenses, zero-dispersion bands, and topological insulators. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal, and photonic metamaterials composed of weakly interacting unit cells.

Guiding energy deliberately is one of the central elements in engineering and information processing. It is often achieved by designing specific transport channels in a suitable material. Topological metamaterials offer a way to construct stable and efficient channels of unprecedented versatility. However, due to their stability it can be tricky to terminate them or to temporarily shut them off without changing the material properties massively. While a lot of effort was put into realizing mechanical topological metamaterials, almost no works deal with manipulating their edge channels in sight of applications. Here, we take a step in this direction, by taking advantage of local symmetry breaking potentials to build a switchable topological phonon channel., Comment: 6 pages, 4 figures; Submitted to New Journal of Physics focus issue on Topological Mechanics

Classifying phases of matter is a central problem in physics. For quantum mechanical systems, this task can be daunting owing to the exponentially large Hilbert space. Thanks to the available computing power and access to ever larger data sets, classification problems are now routinely solved using machine learning techniques. Here, we propose to use a neural network based approach to find phase transitions depending on the performance of the neural network after training it with deliberately incorrectly labelled data. We demonstrate the success of this method on the topological phase transition in the Kitaev chain, the thermal phase transition in the classical Ising model, and the many-body-localization transition in a disordered quantum spin chain. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to a generic tool to identify unexplored phase transitions., Comment: 5 pages, 3 figures

Virtually all interactions that are relevant for atomic and condensed matter physics are mediated by quantum fluctuations of the electromagnetic field vacuum. Consequently, controlling the vacuum fluctuations can be used to engineer the strength and the range of interactions. Recent experiments have used this premise to demonstrate novel quantum phases or entangling gates by embedding electric dipoles in photonic cavities or waveguides, which modify the electromagnetic fluctuations. Here, we show theoretically that the enhanced fluctuations in the anti-squeezed quadrature of a squeezed vacuum state allows for engineering interactions between electric dipoles without the need for a photonic structure. Thus, the strength and range of the interactions can be engineered in a time-dependent way by changing the spatial profile of the squeezed vacuum in a travelling-wave geometry, which also allows the implementation of chiral dissipative interactions. Using experimentally realized squeezing parameters and including realistic losses, we predict single atom cooperativities $C$ of up to 10 for the squeezed vacuum enhanced interactions.

In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Neverethless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher lying bands via perturbative Schrieffer-Wolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian and that the compressibility is diverging as a consequence of an emergent $SU(2)$ symmetry. This symmetry is broken by second order interband transitions resulting in a finite compressibility, which we illustrate for a one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the Marzari-Vanderbilt sense are used. Finally, we prove an important inequality $D \geq \mathcal{W}^2$ between the Drude weight $D$ and the winding number $\mathcal{W}$, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.

We use an external spin as a dynamical probe of many body localization. The probe spin is coupled to an interacting and disordered environment described by a Heisenberg spin chain in a random field. The spin-chain environment can be tuned between a thermalizing delocalized phase and non-thermalizing localized phase, both in its ground- and high-energy states. We study the decoherence of the probe spin when it couples to the environment prepared in three states: the ground state, the infinite temperature state and a high energy N\'eel state. In the non-thermalizing many body localized regime, the coherence shows scaling behaviour in the disorder strength. The long-time dynamics of the probe spin shows a logarithmic dephasing in analogy with the logarithmic growth of entanglement entropy for a bi-partition of a many-body localized system. In summary, we show that decoherence of the probe spin provides clear signatures of many-body localization., Comment: 5 pages, 4 figures