Conformal Floquet dynamics with a continuous drive protocol

Abstract

We study the properties {of a conformal field theory} (CFT) driven periodically with a continuous protocol characterized by a frequency ${\omega }_D$. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator $U$. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for $U$ that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability ($P_n$), equal ($C_n$) and unequal ($G_n$) time two-point primary correlators, energy density($E_n$), and the $m^{\mathrm{th}}$ Renyi entropy ($S_n^m$) after $n$ drive cycles. Our results show that below a crossover stroboscopic time scale $n_c$, $P_n$, $E_n$ and $G_n$ exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of $C_n$, $G_n$ and $E_n$ for the continuous protocol and find emergence of spatial divergences of $C_n$ and $G_n$ in both the heating and non-heating phases. We express our results for $S_n^m$ and $C_n$ in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

20 pages, many figures

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Cited by in corpus (14)

• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• State Dependence of Krylov Complexity in $2d$ CFTs
• 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
• Out-of-Time-Order correlators in driven conformal field theories
• Chaos and operator growth in 2d CFT
• Thermal and dissipative effects on the heating transition in a driven critical system
• Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• Signatures of fragmentation for periodically driven fermions
• Energy Scale Deformation on Regular Polyhedra
• Perfect Wave Transfer in Continuous Quantum Systems