arXiv subjects

Yevgeny Bar Lev

Publications and source records attributed to Yevgeny Bar Lev.

34 records · Page 2Linked to original sources

arXiv2020

Spin transport in disordered long-range interacting spin chain

Using a numerically exact technique we study spin transport and the evolution of spin-density excitation profiles in a disordered spin-chain with long-range interactions, decaying as a power-law, $r^{-α}$ with distance and $α<2$. Our study confirms the prediction of recent theories that the system is delocalized in this parameters regime. Moreover we find that for $α>3/2$ the underlying transport is diffusive with a transient super-diffusive tail, similarly to the situation in clean long-range systems. We generalize the Griffiths picture to long-range systems and show that it captures the essential properties of the exact dynamics.

cond-mat.dis-nn↗

arXiv2020

Multifractality and its role in anomalous transport in the disordered XXZ spin-chain

The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.

cond-mat.dis-nn↗

arXiv2018

Anomalous thermalization and transport in disordered interacting Floquet systems

Local observables in generic periodically driven closed quantum systems are known to relax to values described by periodic infinite temperature ensembles. At the same time, ergodic static systems exhibit anomalous thermalization of local observables and satisfy a modified version of the eigenstate thermalization hypothesis (ETH), when disorder is present. This raises the question, how does the introduction of disorder affect relaxation in periodically driven systems? In this work, we analyze this problem by numerically studying transport and thermalization in an archetypal example. We find that thermalization is anomalous and is accompanied by subdiffusive transport with a disorder dependent dynamical exponent. Distributions of matrix elements of local operators in the eigenbases of a family of effective time-independent Hamiltonians, which describe the stroboscopic dynamics of such systems, show anomalous departures from predictions of ETH signaling that only a modified version of ETH is satisfied. The dynamical exponent is shown to be related to the scaling of the variance of these distributions with system size.

cond-mat.dis-nn↗

arXiv2018

Emergent locality in systems with power-law interactions

Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a "light-cone," a casual structure arising in their relativistic counterparts. Long-range interactions can potentially soften such constraints, allowing almost instantaneous long jumps of particles, thus defying causality. Since interactions decaying as a power-law with distance, $r^{-α}$, are ubiquitous in nature, it is pertinent to understand what is the fate of causality and information spreading in such systems. Using a numerically exact technique we address these questions by studying the out-of-time-order correlation function of a representative generic system in one-dimension. We show that while the interactions are long-range, their effect on information spreading is asymptotically negligible as long as $α>1$. In this range we find a complex compound behavior, where after a short transient a fully local behavior emerges, yielding asymptotic "light-cones" virtually indistinguishable from "light-cones" in corresponding local models. The long-range nature of the interaction is only expressed in the power-law leaking of information from the "light-cone," with the same exponent as the exponent of the interaction, $α$. Our results directly imply that all previously obtained rigorous bounds on information spreading in long-range interacting systems are not tight, and thus could be improved.

cond-mat.dis-nn↗

arXiv2018

Spin transport in long-range interacting one-dimensional chain

We numerically study spin transport and nonequilibrium spin-density profiles in a clean one-dimensional spin-chain with long-range interactions, decaying as a power-law,$r^{-α}$ with distance. We find two distinct regimes of transport: for $α<1/2$, spin excitations relax instantaneously in the thermodynamic limit, and for $α>1/2$, spin transport combines both diffusive and superdiffusive features. We show that while for $α>3/2$ the spin diffusion coefficient is finite, transport in the system is never strictly diffusive, contrary to corresponding classical systems.

cond-mat.dis-nn↗

arXiv2017

Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential

We study the applicability of the time-dependent variational principle in matrix product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time dynamics are known we demonstrate that convergence of long time observables is subtle and needs to be examined carefully. Remarkably, for the disordered nonintegrable system we consider the long time dynamics are in good agreement with the rigorously obtained short time behavior and with previous obtained numerically exact results, suggesting that at least in this case the apparent convergence of this approach is reliable. Our study indicates that while great care must be exercised in establishing the convergence of the method, it may still be asymptotically accurate for a class of disordered nonintegrable quantum systems.

cond-mat.str-el↗

arXiv2017

(Quasi)Periodic revivals in periodically driven interacting quantum systems

Recently it has been shown that interparticle interactions\emph ongenerically\emph default destroy dynamical localization in periodically driven systems, resulting in diffusive transport and heating. In this work we rigorously construct a family of interacting driven systems which are dynamically localized and effectively decoupled from the external driving potential. We show that these systems exhibit tunable periodic or quasiperiodic revivals of the many-body wavefunction and thus\emph onof all\emph default physical observables. By numerically examining spinless fermions on a one dimensional lattice we show that the analytically obtained revivals of such systems remain stable for finite systems with open boundary conditions while having a finite lifetime in the presence of static spatial disorder. We find this lifetime to be inversely proportional to the disorder strength.

cond-mat.dis-nn↗

arXiv2017

Absence of dynamical localization in interacting driven systems

Using a numerically exact method we study the stability of dynamical localization to the addition of interactions in a periodically driven isolated quantum system which conserves only the total number of particles. We find that while even infinitesimally small interactions destroy dynamical localization, for weak interactions density transport is significantly suppressed and is asymptotically diffusive, with a diffusion coefficient proportional to the interaction strength. For systems tuned away from the dynamical localization point, even slightly, transport is dramatically enhanced and within the largest accessible systems sizes a diffusive regime is only pronounced for sufficiently small detunings.

cond-mat.str-el↗

arXiv2017

Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no on finite region default of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.

cond-mat.dis-nn↗

arXiv2017

The Ergodic Side of the Many-Body Localization Transition

Recent studies point towards nontriviality of the ergodic phase in systems exhibiting many-body localization (MBL), which shows subexponential relaxation of local observables, subdiffusive transport and sublinear spreading of the entanglement entropy. Here we review the dynamical properties of this phase and the available numerically exact and approximate methods for its study. We discuss in which sense this phase could be considered ergodic and present possible phenomenological explanations of its dynamical properties. We close by analyzing to which extent the proposed explanations were verified by numerical studies and present the open questions in this field.

cond-mat.dis-nn↗

arXiv2017

Information propagation in isolated quantum systems

Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time-evolution we show that for weakly disordered nonintegrable systems information propagates behind a ballistically moving front, and the entanglement entropy growths linearly in time. For stronger disorder the motion of the information front is algebraic and sub-ballistic and is characterized by an exponent which depends on the strength of the disorder, similarly to the sublinear growth of the entanglement entropy. We show that the dynamical exponent associated with the information front coincides with the exponent of the growth of the entanglement entropy for both weak and strong disorder. We also demonstrate that the temporal dependence of the OTOC is characterized by a fast\emph onnonexponential\emph default growth, followed by a slow saturation after the passage of the information front. Finally,we discuss the implications of this behavioral change on the growth of the entanglement entropy.

cond-mat.dis-nn↗

arXiv2016

Anomalous thermalization in ergodic systems

It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive, since there are systems that are asymptotically in a thermal state, yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the offdiagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the offdiagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus directly violating Berry's conjecture.

cond-mat.stat-mech↗

arXiv2016

Many-Body Localization in System with a Completely Delocalized Single-Particle Spectrum

Many-body localization (MBL) in a one-dimensional Fermi Hubbard model with random on-site interactions is studied. While for this model all single-particle states are trivially delocalized, it is shown that for sufficiently strong disordered interactions the model is many-body localized. It is therefore argued that MBL does not necessary rely on localization of the single-particle spectrum. This model provides a convenient platform to study pure MBL phenomenology, since Anderson localization in this model does not exist. By examining various forms of the interaction term a dramatic effect of symmetries on charge transport is demonstrated. A possible realization in a cold atom experiments is proposed.

cond-mat.dis-nn↗

arXiv2016

Slow Dynamics in a Two-Dimensional Anderson-Hubbard Model

We study the real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small clusters, we demonstrate that for strong disorder this technique approaches the exact result on all available timescales, while for intermediate disorder, in the vicinity of the many-body localization transition, it produces quantitatively accurate results up to nontrivial times. Our method allows for the treatment of system sizes inaccessible by any numerically exact method and for the complete elimination of finite size effects for the times considered. We show that for a sufficiently strong disorder the system becomes nonergodic, while for intermediate disorder strengths and for all accessible time scales transport in the system is strictly subdiffusive. We argue that these results are incompatible with a simple percolation picture, but are consistent with the heuristic random resistor network model where subdiffusion may be observed for long times until a crossover to diffusion occurs. The prediction of slow finite-time dynamics in a two-dimensional interacting and disordered system can be directly verified in future cold atoms experiments

cond-mat.dis-nn↗

arXiv2015

Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice

We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistics of its eigenvalues and its dynamical behavior. We show that the nonergodic phase is reentrant as a function of the interaction strength, illustrating that localization can be reinforced by sufficiently strong interactions even at infinite temperature. Surprisingly, within the accessible time range, the ergodic phase shows subdiffusive behavior, suggesting that the diffusion coefficient vanishes throughout much of the phase diagram in the thermodynamic limit. Our findings strongly suggest that Wigner-Dyson statistics of eigenvalue spacings may appear in a class of ergodic but subdiffusive systems.

cond-mat.dis-nn↗

arXiv2014

Dynamics of Many-Body Localization

Following the field theoretic approach of Basko et al., Ann. Phys. 321, 1126 (2006), we study in detail the real-time dynamics of a system expected to exhibit many-body localization. In particular, for time scales inaccessible to exact methods, we demonstrate that within the second-Born approximation that the temporal decay of the density-density correlation function is non-exponential and is consistent with a finite value for $t\to\infty$, as expected in a non-ergodic state. This behavior persists over a wide range of disorder and interaction strengths. We discuss the implications of our findings with respect to dynamical phase boundaries based both on exact diagonalization studies and as well as those established by the methods of Ref. 1.

cond-mat.dis-nn↗