Classification of $SL_2$ deformed Floquet Conformal Field Theories

TL;DR

This paper classifies the stability of (1+1)D conformal field theories under periodic $SL_2$ deformed Hamiltonian driving, revealing conditions for non-heating phases and showing the phase diagram's dependence on the driving Hamiltonians.

Contribution

It provides a comprehensive classification of stability phases in $SL_2$ deformed Floquet CFTs, including necessary and sufficient conditions for non-heating phases.

Findings

Heating phase is generally dominant in the phase diagram.

Non-heating phases may be absent depending on the Hamiltonian types.

Conditions for non-heating phases are explicitly derived for N=2 and N>2.

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 $SL_2$ 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 $N=1$.