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arXiv:1706.05026 · Physical review. B./Physical review. B

Slow dynamics in translation-invariant quantum lattice models

Alexios A. Michailidis, Marko Žnidarič, Mariya V. Medvedyeva, Dmitry A. Abanin, Tomaž Prosen, Zlatko Papić

Published Mar 19, 2018• 42 citations
arXivHTMLPDF

Abstract

Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of the robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiments and numerical simulations.

DOI
10.1103/physrevb.97.104307

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Recently it has been suggested that many-body localization (MBL) can occur in translationally-invariant systems, and candidate 1D models have been proposed. We find that such models typically exhibit strong finite-size effects due to the presence of two or more vastly different energy scales, including an artificial separation of density of states into bands separated by large energy gaps. By carefully choosing the parameters of the models such that finite-size effects are minimized, we perform extensive numerical studies of small systems using exact diagonalization. Based on the variety of diagnostics, including entanglement properties and the behavior of local observables, we find the systems exhibit thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translationally-invariant systems with two very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
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Understanding the spread of quantum entanglement and scrambling of information across a quantum many-body system is a fundamental problem in quantum dynamics. A necessary part of the spread of the entanglement is the growth in time of Heisenberg operators of initially localized operators. This operator growth can be diagnosed by studying the space-time structure of commutators of well-separated operators. Previous studies in this area focused on translation invariant models, but the effects of disorder, which can radically alter the motion of heat and charge, had not been studied. Here, the authors study the growth of operators in interacting systems with quenched disorder. In the localized phase, they find that operator sizes grow logarithmically in time similar to other measures of entanglement spreading. In the disordered metal, they find that operator sizes grow linearly with time, i.e., ballistically, in contrast to the diffusive motion of charge and heat. The ballistic growth of operators is quantified by the butterfly velocity which the authors relate to the charge diffusion constant and the interaction-induced inelastic scattering rate. When the diffusion of charge is slow, the resulting butterfly velocity is much smaller than the maximum speed allowed by microscopic causality constraints.
Interacting many-body quantum systems and their dynamics, while fundamental to modern science and technology, are formidable to simulate and understand. However, by discovering their symmetries, conservation laws, and integrability, one can unravel their intricacies. Here, using up to 124 qubits of a fully programmable quantum computer, we uncover local conservation laws and integrability in one- and two-dimensional periodically-driven spin lattices in a regime previously inaccessible to such detailed analysis. We focus on the paradigmatic example of disorder-induced ergodicity breaking, where we first benchmark the system crossover into a localized regime through anomalies in the one-particle-density-matrix spectrum and other hallmark signatures. We then demonstrate that this regime stems from hidden local integrals of motion by faithfully reconstructing their quantum operators, thus providing a more detailed portrait of the system’s integrable dynamics. Our results demonstrate a versatile strategy for extracting the hidden dynamical structure from noisy experiments on large-scale quantum computers. Local integrals of motion are useful for understanding emergent integrability in many-body localized systems. Here the authors use a large-scale superconducting quantum processor with up to 124 qubits to simulate many-body dynamics in 1D and 2D systems and demonstrate extraction of local integrals of motion.