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.

15 pages, REVTeX, 11 figures; final published version

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• 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
• 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
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• Marginal quenches and drives in Tomonaga-Luttinger 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