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arXiv:2012.05753 · Physical Review Research

Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium

Guoyi Zhu, Markus Heyl

Published Sep 17, 2021• 19 citations
arXivHTMLPDF

Abstract

Disorder-free localization has recently emerged as a mechanism for ergodicity breaking in homogeneous lattice gauge theories.In this work we show that this mechanism can lead to unconventional states of quantum matter as the absence of thermalization lifts constraints imposed by equilibrium statistical physics.We study a Kitaev honeycomb model in a skew magnetic field subject to a quantum quench from a fully polarized initial product state and observe nonergodic dynamics as a consequence of disorder-free localization.We find that the system exhibits a subballistic power-law entanglement growth and quantum correlation spreading, which is otherwise typically associated with thermalizing systems.In the asymptotic steady state the Kitaev model develops volume-law entanglement and power-law decaying dimer quantum correlations even at a finite energy density.Our work sheds light on the potential for disorder-free localized lattice gauge theories to realize quantum states in two dimensions with properties beyond what is possible in an equilibrium context.

DOI
10.1103/physrevresearch.3.l032069

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Disorder-free localization has recently emerged as a mechanism for ergodicity breaking in homogeneous lattice gauge theories.In this work we show that this mechanism can lead to unconventional states of quantum matter as the absence of thermalization lifts constraints imposed by equilibrium statistical physics.We study a Kitaev honeycomb model in a skew magnetic field subject to a quantum quench from a fully polarized initial product state and observe nonergodic dynamics as a consequence of disorder-free localization.We find that the system exhibits a subballistic power-law entanglement growth and quantum correlation spreading, which is otherwise typically associated with thermalizing systems.In the asymptotic steady state the Kitaev model develops volume-law entanglement and power-law decaying dimer quantum correlations even at a finite energy density.Our work sheds light on the potential for disorder-free localized lattice gauge theories to realize quantum states in two dimensions with properties beyond what is possible in an equilibrium context.
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We study quantum quenches in two-dimensional lattice gauge theories with fermions coupled to dynamical Z2{\mathbb{Z}}_{2}Z2​ gauge fields. Through the identification of an extensive set of conserved quantities, we propose a generic mechanism of charge localization in the absence of quenched disorder both in the Hamiltonian and in the initial states. We provide diagnostics of this localization through a set of experimentally relevant dynamical measures, entanglement measures, as well as spectral properties of the model. One of the defining features of the models that we study is a binary nature of emergent disorder, related to Z2{\mathbb{Z}}_{2}Z2​ degrees of freedom. This results in a qualitatively different behavior in the strong disorder limit compared to typically studied models of localization. For example, it gives rise to a possibility of a delocalization transition via a mechanism of quantum percolation in dimensions higher than 1D. We highlight the importance of our general phenomenology to questions related to dynamics of defects in Kitaev's toric code, and to quantum quenches in Hubbard models. While the simplest models we consider are effectively noninteracting, we also include interactions leading to many-body localizationlike logarithmic entanglement growth. Finally, we consider effects of interactions that generate dynamics for conserved charges, which gives rise to only transient localization behavior, or quasi-many-body localization.
Lattice gauge theories, the discrete counterparts of continuum gauge theories, provide a rich framework for studying non-equilibrium quantum dynamics. Recent studies suggest disorder-free localization in the lattice Schwinger model, but its origin remains unclear. Using a combination of analytical and numerical methods, we show that Hilbert space fragmentation emerges in the strong coupling limit, constraining particle dynamics and causing sharp jumps in entanglement entropy growth within charge sectors. By analyzing jump statistics, we find that entanglement growth follows a single-logarithmic or weak power-law dependence on time, rather than a double-logarithmic form. This suggests a single ergodicity-breaking regime that mimics many-body localization in finite systems due to fragmentation effects. Our findings clarify the nature of disorder-free localization and its distinction from conventional many-body localization, highlighting how gauge constraints influence thermalization in lattice gauge theories.
We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.
Disorder-free localization has been proposed as a mechanism for ergodicity breaking in lattice gauge theories (LGTs) which can even occur in two spatial dimensions (2D). It has been shown that the U(1) quantum link model (QLM) can localize due to an emergent classical percolation transition fragmenting the system into disconnected real-space clusters. While the nature of the quantum localization transition (QLT) is still debated for conventional many-body localization, here we provide a comprehensive characterization of the QLT for the QLM in 2D for a disorder-free case. In this Letter we find compelling evidence that the QLT in the 2D QLM is continuous and we determine its universality class. We base our considerations on a spectral analysis of finite-size clusters in the percolation problem which exhibits two regimes---one in which large clusters effectively behave nonergodically, a result naturally accounted for as an interference phenomenon in configuration space, and the other in which all large clusters behave ergodically. Our analysis can also be applied to other 2D U(1) LGTs potentially including also matter degrees of freedom.
Disorder-free localization is a paradigm of strong ergodicity breaking that has been shown to occur in global quenches of lattice gauge theories when the system is initialized in a superposition over an extensive number of gauge sectors. Here, we show that preparing the system in a thermal Gibbs ensemble without any coherences between different gauge sectors also gives rise to disorder-free localization, with temperature acting as a disorder strength. We demonstrate our findings by calculating the quench dynamics of the imbalance of thermal ensembles in both U(1)\mathrm{U}(1)U(1) and Z2\mathbb{Z}_2Z2​ lattice gauge theories through exact diagonalization, showing greater localization with increasing ensemble temperature. Furthermore, we show how adding terms linear in local pseudogenerators can enhance temperature-induced disorder-free localization due to the dynamical emergence of an enriched local symmetry. Our work expands the realm of disorder-free localization into finite-temperature physics, and shows counterintuitively that certain quantum nonergodic phenomena can become more prominent at high temperature. We discuss the accessibility of our conclusions in current quantum simulation and computing platforms.