Geometric approach to inhomogeneous Floquet systems

TL;DR

This paper introduces a geometric framework for analyzing inhomogeneous Floquet many-body systems in 1+1D conformal field theory, revealing complex phase structures and transitions between heating and nonheating states.

Contribution

It develops a novel geometric approach based on circle dynamical systems that generalizes previous algebraic methods, applicable to a broader class of inhomogeneous Floquet systems.

Findings

Identification of fixed and higher-periodic points as indicators of heating phases

Discovery of cusps in the heating rate indicating phase transitions

Rich phase diagrams with Lifshitz-like transitions detectable via entanglement entropy kinks

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.