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Phase Structure of Driven Quantum Systems.

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TLDR
It is shown that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions, and these are analogs of equilibrium states with broken symmetries and topological order.
Abstract
Clean and interacting periodically driven systems are believed to exhibit a single, trivial "infinite-temperature" Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions. Some of these are analogs of equilibrium states with broken symmetries and topological order, while others-genuinely new to the Floquet problem-are characterized by order and nontrivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.

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Colloquium: Many-body localization, thermalization, and entanglement

TL;DR: Theoretically, many-body localized (MBL) systems exhibit a new kind of robust integrability: an extensive set of quasilocal integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization as mentioned in this paper.
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Observation of a discrete time crystal

TL;DR: In this paper, the authors present the experimental observation of a discrete time crystal in an interacting spin chain of trapped atomic ions and apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations.
Journal ArticleDOI

Observation of discrete time-crystalline order in a disordered dipolar many-body system

TL;DR: This work observes long-lived temporal correlations, experimentally identifies the phase boundary and finds that the temporal order is protected by strong interactions, which opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.
Journal ArticleDOI

Topological phases of non-Hermitian systems

TL;DR: In this article, a coherent framework of topological phases of non-Hermitian Hamiltonians was developed, and the K-theory was applied to systematically classify all the topology phases in the Altland-Zirnbauer classes in all dimensions.
Journal ArticleDOI

Topological Phases of Non-Hermitian Systems

TL;DR: In this paper, a coherent framework of topological phases of non-Hermitian Hamiltonians was developed, and the K-theory was applied to systematically classify all the topology phases in the Altland-Zirnbauer classes in all dimensions.
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