Geometric approach to inhomogeneous Floquet systems

Abstract

We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical systems on the circle that we establish and use to prove existence of (non)heating phases characterized by the (absence) presence of fixed or higher-periodic points of coordinate transformations encoding the time evolution: Heating corresponds to energy and excitations concentrating exponentially fast at unstable such points while nonheating to pseudoperiodic motion. We show that the heating rate (serving as the order parameter for transitions between these two) can have cusps, even within the overall heating phase, and that there is a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. Our geometric approach generalizes previous results for a subfamily of similar systems that used only the $\mathfrak{sl}(2)$ algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it has wider applicability, even beyond conformal field theory.

arXiv comment15 pages, REVTeX, 11 figures; final published version

References in corpus (45)

• Photonic Floquet Topological Insulators
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Topological characterization of periodically-driven quantum systems
• Observation of a Discrete Time Crystal
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• On the phase structure of driven quantum systems
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Nonlinear phononics: A new ultrafast route to lattice control
• Many-body localization in periodically driven systems
• Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5
• Exponentially slow heating in periodically driven many-body systems
• Quantum quenches in 1+1 dimensional conformal field theories
• Photonic Topological Anderson Insulators
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• A theory of many-body localization in periodically driven systems
• Quantum Generalized Hydrodynamics
• Inhomogeneous field theory inside the arctic circle
• Heating and many-body resonances in a periodically driven two-band system
• A Floquet Model for the Many-Body Localization Transition
• Integrable Floquet dynamics
• Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
• Pump frequency resonances for light-induced incipient superconductivity in YBa${}_2$Cu${}_3$O${}_{6.5}$
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Quantized magnetization density in periodically driven systems
• Bulk-Edge correspondence for two-dimensional Floquet topological insulators
• Emergent Black Hole Dynamics in Critical Floquet Systems
• Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
• Finite-time universality in nonequilibrium CFT
• Inhomogeneous conformal field theory out of equilibrium
• Time evolution of the Luttinger model with nonuniform temperature profile
• Diffusive Heat Waves in Random Conformal Field Theory
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Many-body Dynamics with Time-dependent Interaction
• Deterministic chaos and fractal entropy scaling in Floquet CFT
• Scaling of entanglement entropy across Lifshitz transitions
• Geometrizing quantum dynamics of a Bose-Einstein condensate
• Floquet dynamics of classical and quantum cavity fields
• Periodically and Quasi-periodically Driven Dynamics of Bose-Einstein Condensates
• Floquet conformal field theory

Cited by in corpus (26)

• Floquet conformal field theories with generally deformed Hamiltonians
• Inhomogeneous conformal field theory out of equilibrium
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• Entanglement and geometry from subalgebras of the Virasoro algebra
• Quantum information geometry of driven CFTs
• Holographic Quantum Scars
• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
• Out-of-Time-Order correlators in driven conformal field theories
• The Real-Time Correlation Function of Floquet Conformal Fields
• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• Thermal and dissipative effects on the heating transition in a driven critical system
• Marginal quenches and drives in Tomonaga-Luttinger liquids
• Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
• Bridging two quantum quench problems -- local joining quantum quench and Möbius quench -- and their holographic dual descriptions
• Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Floquet engineered inhomogeneous quantum chaos in critical systems
• Periodically driven perturbed CFTs: the sine-Gordon model
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches
• Driven Non-Unitary Dynamics of Quantum Critical Systems
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids
• Stability of the classical catenoid and Darboux-Pöschl-Teller potentials