arXiv subjects

Richard Berkovits

Publications and source records attributed to Richard Berkovits.

At least 19 recordsLinked to original sources

arXiv2026

Localization and Flat Bands in Bond-Inflated Lattices

We study localization and flat-band formation in lattices generated by repeated bond inflation of square, honeycomb, and triangular parent lattices. Replacing each bond by a finite tight-binding chain produces several distinct classes of flat bands: chain-induced flat bands at the eigenenergies of the inserted chains, symmetry-protected zero-energy flat bands in bipartite bond-inflated lattices, and nearly flat junction bands near the spectral edges for sufficiently long chains. We analyze these mechanisms for ordered Lieb-$L$, super$^{L}$honeycomb, and super$^{L}$triangular lattices, and examine their response to bond disorder, site disorder, random magnetic flux, and randomness in the inflation process itself. While bond and site disorder broaden most flat bands, the zero-energy chiral band and the junction-induced flat bands remain robust under certain perturbations. Remarkably, substantial flat-band features also persist in randomly bond-inflated graphs, even in the absence of translational symmetry. In particular, the number of zero-energy states is found to be well estimated by the matching deficiency $N-2ν(G)$, indicating that local tree-like structure continues to control the low-energy nullity. These results identify bond-inflated lattices as a broad class of systems in which geometry alone generates robust localization in both ordered and random settings.

cond-mat.dis-nn↗

arXiv2025

The Smearing of Quasi-Particles: Signatures in the Entanglement Entropy of Excited Many-Particle Systems

The entanglement spectrum serves as a powerful tool for probing the structure and dynamics of quantum many-body systems, revealing key information about symmetry, topology, and excitations. While the entanglement entropy (EE) of ground states typically follows an area law, highly excited states obey a volume law, leading to a striking contrast in their scaling behavior. In this paper, we investigate the crossover between these two regimes, focusing on the role of quasi-particles (QPs) in mediating this transition. By analyzing the energy dependence of EE in various many-body systems, we explore how the presence of long-lived QPs influences the entanglement structure of excited states. We present numerical results for spinless fermions, a spin chain near a many-body localization transition, and the Sachdev-Ye-Kitaev (SYK) model, which lacks a conventional QP description. Our findings are complemented by a theoretical model based on Fermi liquid theory, providing insight into the interaction-dependent scaling of EE and its consistency with numerical simulations. We find that a hallmark of QPs is a linear dependence of the eigenstate EE on energy, which breaks down at high energy and in the limit of strong interaction. The slope of this linear dependence reflects the QP weight, which reduces with interaction strength.

cond-mat.quant-gas↗

arXiv2024

Unraveling Complexity: Singular Value Decomposition in Complex Experimental Data Analysis

Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses conventional approaches in understanding complex physics data. Singular values and vectors distinguish and highlight various physical mechanisms and scales, revealing previously challenging elements. SVD emerges as a powerful tool for navigating complex experimental landscapes, showing promise for diverse experimental measurements.

physics.data-an↗

arXiv2024

Inducing a Metal-Insulator Transition through Systematic Alterations of Local Rewriting Rules in a Quantum Graph

The Anderson localization transition in quantum graphs has garnered significant recent attention due to its relevance to many-body localization studies. Typically, graphs are constructed using top-down methods. Here, we explore a bottom-up approach, employing a simple local rewriting rule to construct the graph. Through the use of ratio statistics for the energy spectrum and Kullback-Leibler divergence correlations for the eigenstates, numerical analysis demonstrates that slight adjustments to the rewriting rule can induce a transition from a localized to an extended quantum phase. This extended state exhibits non-ergodic behavior, akin to the non-ergodic extended phase observed in the Porter-Rosenzweig model and suggested for many-body localization. Thus, by adapting straightforward local rewriting rules, it becomes feasible to assemble complex graphs from which desired global quantum phases emerge. This approach holds promise for numerical investigations and could be implemented in building optical realizations of complex networks using optical fibers and beam splitters.

cond-mat.dis-nn↗

arXiv2024

Randomly Pruning the Sachdev-Ye-Kitaev model

The Sachdev-Ye-Kitaev model (SYK) is renowned for its short-time chaotic behavior, which plays a fundamental role in its application to various fields such as quantum gravity and holography. The Thouless energy, representing the energy scale at which the universal chaotic behavior in the energy spectrum ceases, can be determined from the spectrum itself. When simulating the SYK model on classical or quantum computers, it is advantageous to minimize the number of terms in the Hamiltonian by randomly pruning the couplings. In this paper, we demonstrate that even with a significant pruning, eliminating a large number of couplings, the chaotic behavior persists up to short time scales This is true even when only a fraction of the original $O(L^4)$ couplings in the fully connected SYK model, specifically $O(KL)$, is retained. Here, $L$ represents the number of sites, and $K\sim 10$. The properties of the long-range energy scales, corresponding to short time scales, are verified through numerical singular value decomposition (SVD) and level number variance calculations.

cond-mat.str-el↗

arXiv2023

Unfolding a composed ensemble of energy spectra using singular value decomposition

In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an ensemble where there are large realization-to-realization fluctuations the canonical methods for unfolding fail. Here we show that singular value decomposition can be used even for the challenging situations where the ensemble is composed out of realizations originating from a different range of parameters resulting in a non-monotonous local density of states. This can be useful in experimental situations for which the physical parameters can not be tightly controlled, of for situations for which the local density of states is strongly fluctuating.

cond-mat.dis-nn↗

arXiv2022

Sachdev-Ye-Kitaev model: Non-self-averaging properties of the energy spectrum

The short time (large energy) behavior of the Sachdev-Ye-Kitaev model (SYK) is one of the main motivation to the growing interest garnered by this model. True chaotic behaviour sets in at the Thouless time, which can be extracted from the energy spectrum. In order to do so, it is necessary to unfold the spectrum, i.e., to filter out global tendencies. Using a simple ensemble average for unfolding results in a parametically low estimation of the Thouless energy. By examining the behavior of the spectrum as the distribution of the matrix elements is changed into a log-normal distribution it is shown that the sample to sample level spacing variance determines this estimation of the Thouless energy. Using the singular value decomposition method, SVD, which filters out these sample to sample fluctuations, the Thouless energy becomes parametrically much larger, essentially of order of the band width. It is shown that the SYK model in non-self-averaging even in the thermodynamic limit which must be taken into account in considering its short time properties.

cond-mat.dis-nn↗

arXiv2022

Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields

In recent years it became clear that the metallic regime of systems that exhibit a many body localization (MBL) behavior show properties which are quite different than the vanilla metallic region of the single particle Anderson regime. Here we show that the large scale energy spectrum of a canonical microscopical model featuring MBL, displays a non-universal behavior at intermediate scales, which is distinct from the deviation from universality seen in the single particle Anderson regime. The crucial step in revealing this behavior is a global unfolding of the spectrum performed using the singular value decomposition (SVD) which takes into account the sample to sample fluctuations of the spectra. The spectrum properties may be observed directly in the singular value amplitudes via the scree plot, or by using the SVD to unfold the spectra and then perform a number of states variance calculation. Both methods reveal an intermediate scale of energies which follow super Posissonian statistics.

cond-mat.dis-nn↗

arXiv2021

Probing the metallic energy spectrum beyond the Thouless energy scale using the singular value decomposition

Disordered quantum systems feature an energy scale know as the Thouless energy. For energy ranges below this scale, the properties of the energy spectrum can be described by random matrix theory. Above this scale a different behavior sets in. For a metallic system it has been long ago shown by Altshuler and Shklovskii that the number variance should increase as a power law with a power dependent only on the dimensionality of the system. Although tantalizing hints for this behavior have been seen in previous numerical studies, it is quite difficult to verify this prediction using the standard local unfolding methods. Here we use a different unfolding method, i.e., the singular value decomposition, and establish a connection between the power law behavior of the scree plot (the singular values ranked by their amplitude) and the power law behavior of the number variance. Thus we are able to numerically verify the Altshuler and Shklovskii's prediction for disordered $3D$, $4D$, and $5D$ single-electron Anderson models on square lattices in the metallic regime. The same method could be applied to systems such as the Sachdev-Ye-Kitaev model and various interacting many body models for which the many body localization occurs. It has been recently reported that such systems exhibit a Thouless energy and analyzing the spectrum's behavior on larger scales is of much current interest.

cond-mat.mes-hall↗

arXiv2020

Universal Voltage Fluctuations in Disordered Superconductors

The Aharonov-Casher effect is the analogue of the Aharonov-Bohm effect that applies to neutral particles carrying a magnetic moment. This can be manifested by vortices or fluxons flowing in trajectories that encompass an electric charge. These have been predicted to result in a persistent voltage which fluctuates for different sample realizations. Here we show that disordered superconductors exhibit reproducible voltage fluctuation, antisymmetrical with respect to magnetic field, as a function of various parameters such as magnetic field amplitude, field orientations and gate voltage. These results are interpreted as the vortex equivalent of the universal conductance fluctuations typical of mesoscopic disordered metallic systems. We analyze the data in the framework of random matrix theory and show that the fluctuation correlation functions and curvature distributions exhibit behavior which is the fingerprint of Aronov-Casher physics. The results demonstrate the quantum nature of the vortices in highly disordered superconductors both above and below $T_c$.

cond-mat.supr-con↗

arXiv2020

On super-Poissonian behavior of the Rosenzweig-Porter model in the non-ergodic extended regime

The Rosenzweig-Porter model has seen a resurgence in interest as it exhibits a non-ergodic extended phase between the ergodic extended metallic phase and the localized phase. Such a phase is relevant to many physical models from the Sachdev-Ye-Kitaev model in high-energy physics and quantum gravity, to the interacting many-body localization in condensed matter physics and quantum computing. This phase is characterized by fractal behavior of the wavefunctions, and a postulated correlated mini-band structure of the energy spectrum. Here we will seek evidence for the latter in the spectrum. Since this behavior is expected on intermediate energy scales spectral rigidity is a natural way to tease it out. Nevertheless, due to the Thouless energy and ambiguities in the unfolding procedure, the results are inconclusive. On the other hand, by using the singular value decomposition method, clear evidence for a super-Poissonian behavior in this regime emerges, consistent with a picture of correlated mini-bands.

cond-mat.dis-nn↗

arXiv2019

Emergent bosons in the fermionic two-leg flux ladder

We study the emergence of bosonic pairs in a system of two coupled one-dimensional fermionic chains subject to a gauge flux (two-leg flux ladder), with both attractive and repulsive interaction. In the presence of strong attractive nearest-neighbor interaction and repulsive next-to-nearest-neighbor interaction, the system crosses into a regime in which fermions form tightly bound pairs, which behave as bosonic entities. By means of numerical simulations based on the density-matrix-renormalization-group (DMRG) method, we show in particular that in the strongly paired regime, the gauge flux induces a quantum phase transition of the Ising type from vortex density wave (VDW) to a charge density wave (CDW), characteristic of bosonic systems.

cond-mat.str-el↗

arXiv2018

Extracting many-particle entanglement entropy from observables using supervised machine learning

Entanglement, which quantifies non-local correlations in quantum mechanics, is the fascinating concept behind much of aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is very challenging. Here we show that via supervised machine learning using a convolutional neural network, we can infer the entanglement from a measurable observable for a disordered interacting quantum many-particle system. Several structures of neural networks were tested and a convolutional neural network akin to structures used for image and speech recognition performed the best. After training on a set of 500 realizations of disorder, the network was applied to 200 new realizations and its results for the entanglement entropy were compared to a direct computation of the entanglement entropy. Excellent agreement was found, except for several rare region which in a previous study were identified as belonging to an inclusion of a Griffiths-like quantum phase. Training the network on a test set with different parameters (in the same phase) also works quite well.

cond-mat.dis-nn↗

arXiv2017

On low eigevalues of the entanglement Hamiltonian, localization length, and rare regions in disordered interacting one-dimensional systems

The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of disordered interacting one-dimensional many-particle system is studied. The average of the first entanglement Hamiltonian level spacing is proportional to the ground state localization length and shows the same dependence on the disorder and interaction strength as the localization length. This is the result of the fact that entanglement is limited to distances of order of the localization length. The distribution of the first entanglement level spacing shows a Gaussian-like behavior as expected for level spacings much larger than the disorder broadening. For weakly disordered systems (localization length larger than sample length), the distribution shows an additional peak at low level spacings. This stems from rare regions in some samples which exhibit metallic-like behavior of large entanglement and large particle number fluctuations. These intermediate 'microemulsion' metallic regions embedded in the insulating phase are discussed.

cond-mat.mes-hall↗

arXiv2015

Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane's conjecture on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. In order to demonstrate the correspondence we develop a computational efficient way to calculate the ES of low-excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation structure. The low-lying shell are robust and survive even for strong electron-electron interactions.

cond-mat.dis-nn↗

arXiv2015

Entanglement properties and quantum phases for a fermionic disordered one dimensional wire with attractive interactions

A fermionic disordered one dimensional wire in the presence of attractive interactions is known to have two distinct phases: A localized and a superconducting one depending on the strength of interaction and disorder. The localized region may also exhibit a metallic behaviour if the system size is shorter than the localization length. Here we show that the superconducting phase has a distinct distribution of the entanglement entropy and entanglement spectrum distinct from the metallic regime. The entanglement entropy distribution is strongly asymmetric with Lévy alpha stable distribution (compared to the Gaussian metallic distribution), and the entanglement level spacing distribution is unitary (compared to orthogonal). Thus, entanglement properties may reveal properties which can not be detected by other methods.

cond-mat.mes-hall↗

arXiv2015

Entanglement Entropy on the Cayley Tree

The properties of the entanglement entropy (EE) of a clean Cayley tree (CT) are studied. The EE shows a completely different behaviour depending on the way the CT is partitioned into two regions and whether we consider the ground-state or highly excited many-particle wave function. The ground-state EE increases logarithmically as function of number of generation if a single branch is pruned off the tree, while it grows exponentially if the region around the root is trimmed. On the other hand, in both cases the highly excited states' EE grows exponentially. Implications of these results to general graphs and disordered systems are shortly discussed.

cond-mat.dis-nn↗

arXiv2015

Compressibility enhancement in an almost staggered interacting Harper model

We discuss the compressibility in the almost staggered fermionic Harper model with repulsive interactions in the vicinity of half-filling. It has been shown by Kraus et al. [33] that for spinless electrons and nearest neighbors electron-electron interactions the compressibility in the central band is enhanced by repulsive interactions. Here we would like to investigate the sensitivity of this conclusion to the spin degree of freedom and longer range interactions. We use the Hartree-Fock (HF) approximation, as well as density matrix renormalization group (DMRG) calculation to evaluate the compressibility. In the almost staggered Harper model, the central energy band is essentially flat and separated from the other bands by a large gap and therefore, the HF approximation is rather accurate.In both cases the compressibility of the system is enhanced compare to the non-interacting case, although the enhancement is weaker due to the inclusion of Hubbard and longer ranged interactions.

cond-mat.mes-hall↗