Chiral Floquet Phases of Many-body Localized Bosons

Abstract

We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL) in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry, and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models, and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

arXiv comment(18+11) pages; (9+2) figures. v2: Minor changes, references updated. v3: References updated, additional discussion on interacting fermions

References in corpus (47)

• Anyons in an exactly solved model and beyond
• The density-matrix renormalization group in the age of matrix product states
• Floquet Topological Insulator in Semiconductor Quantum Wells
• The many-body localization phase transition
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological characterization of periodically-driven quantum systems
• Exploring the many-body localization transition in two dimensions
• Floquet Time Crystals
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• On the phase structure of driven quantum systems
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Long-time behavior of periodically driven isolated interacting lattice systems
• Many-body localization in periodically driven systems
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Ultracold Atoms in a Tunable Optical Kagome Lattice
• Localization protected quantum order
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Exponentially slow heating in periodically driven many-body systems
• Fate of many-body localization under periodic driving
• Three-Dimensional Anderson Localization of Ultracold Matter
• Matrix product operator representations
• Many-body localization in one dimension as a dynamical renormalization group fixed point
• Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• Disorder-induced Localization in a Strongly Correlated Atomic Hubbard Gas
• Disorder-induced Floquet Topological Insulators
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Many-body Localization and Symmetry Protected Topological Order
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• A theory of many-body localization in periodically driven systems
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• Thermal transport in a Luttinger liquid
• Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance
• Index theory of one dimensional quantum walks and cellular automata
• Many body localization and thermalization: insights from the entanglement spectrum
• Abelian Floquet symmetry-protected topological phases in one dimension
• Generalizations and limitations of string-net models
• Many-body localization beyond eigenstates in all dimensions
• Marginal Anderson localization and many body delocalization
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• General theory of many body localized systems coupled to baths
• Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings

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