Floquet conformal field theories with generally deformed Hamiltonians

TL;DR

This paper explores the non-equilibrium dynamics of Floquet conformal field theories with generalized, spatially modulated Hamiltonians, revealing a rich phase diagram with heating and non-heating phases characterized by entanglement and energy distribution patterns.

Contribution

It extends previous work by solving Floquet CFTs with arbitrary smooth deformations involving the full Virasoro algebra, using a geometrical approach to analyze phase transitions.

Findings

The phase diagram is governed by stroboscopic operator trajectories.

Presence of spatial fixed points distinguishes heating from non-heating phases.

Multiple heating phases exhibit different entanglement and energy distribution patterns.

Abstract

In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.