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 experimentsComment: Title change and minor changes in the tex

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.Comment: We trade the discussion of a diffusive integrable system in favor of a discussion of diffusive nonintegrable system, which better highlights the outcome of our wor

Gaussian state approximation of quantum many-body scars

Quantum many-body scars are atypical, highly nonthermal eigenstates of kinetically constrained systems embedded in a sea of thermal eigenstates. These special eigenstates are characterized, for example, by a bipartite entanglement entropy that scales as most logarithmically with subsystem size. We use numerical optimization techniques to investigate if quantum many-body scars of the experimentally relevant PXP model are well approximated by Gaussian states. These states are described by a number of parameters that scales quadratically with system size, thereby having a much lower complexity than generic quantum many-body states. We find that this is a good description for the quantum many-body scars away from the center of the spectrum.Comment: 6 pages, 4 figure

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.Comment: Scipost resubmission. 14 pages, 4 figures. Changes to the figures. Corrects a few typo

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.Comment: 13 pages, 8 figure