Classification of $S{L}_2$ deformed Floquet Conformal Field Theories

Abstract

Classification of the non-equilibrium quantum many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this work, we study the basic question that whether a (1+1) dimensional conformal field theory (CFT) is stable or not under a periodic driving with $N$ non-commuting Hamiltonians. Previous works showed that a Floquet (or periodically driven) CFT driven by certain $S{L}_2$ deformed Hamiltonians exhibit both non-heating (stable) and heating (unstable) phases. In this work, we show that the phase diagram depends on the types of driving Hamiltonians. In general, the heating phase is generic, but the non-heating phase may be absent in the phase diagram. For the existence of the non-heating phases, we give sufficient and necessary conditions for $N=2$, and sufficient conditions for $N>2$. These conditions are composed of $N$ layers of data, with each layer determined by the types of driving Hamiltonians. Our results also apply to the single quantum quench problem with $N=1$.

arXiv comment16 pages

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• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Geometric approach to inhomogeneous Floquet systems
• 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
• Quantum information geometry of driven CFTs
• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
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• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
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• Topological edge states at Floquet quantum criticality
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• Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
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• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• 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
• Energy Scale Deformation on Regular Polyhedra
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States