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arXiv:1412.3117 · Physical Review X

Theory of the Many-Body Localization Transition in One-Dimensional Systems

Ronen Vosk, David A. Huse, Ehud Altman

Published Sep 14, 2015• 401 citations
arXivHTMLPDF

Abstract

The dynamical behavior of quantum systems is relevant to quantum information processing. A new theoretical model describes a phase transition from many-body localized states, in which quantum information is accessible, to thermal states, in which such information is lost in the dynamics.
DOI
10.1103/physrevx.5.031032

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Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in extended quantum systems far from the zero-temperature limit. It separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (``ergodic'') phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present numerical evidence that many-body localization also occurs in models without disorder but rather a quasiperiodic potential. In one dimension, these systems already have a single-particle localization transition, and we show that this transition becomes a many-body localization transition upon the introduction of interactions. We also comment on possible relevance of our results to experimental studies of many-body dynamics of cold atoms and nonlinear light in quasiperiodic potentials.
In thermal phases, the quantum coherence of individual degrees of freedom is rapidly lost to the environment. Many-body localized (MBL) phases limit the spread of this coherence and appear promising for quantum information applications. However, such applications require not just long coherence times but also a means to transport and manipulate information. We demonstrate that this can be done in a one dimensional model of interacting spins at infinite temperature. Our protocol utilizes protected qubits which emerge at the boundary between topological and trivial phases. State transfer occurs via dynamic shifts of this boundary and is shown to preserve quantum information. As an example, we discuss the implementation of a universal, two-qubit gate based upon MBL-protected quantum state transfer.
The authors study the phase transition between thermal and many-body localized phases in one-dimensional systems with quenched randomness and short-range interactions. The approach uses a renormalization group model, very similar to those of previous works, that puts the avalanche instability of the many-body localized phase at center stage. Within that model, the universal critical behavior is determined analytically, and the phase transition is found to belong to a new universality class that differs from the previously found Kosterlitz-Thouless result in important ways.
We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.