Notes on heating phase dynamics in Floquet CFTs and Modular quantization

TL;DR

This paper investigates the heating phase dynamics of Floquet conformal field theories, revealing connections to modular Hamiltonians, holographic entanglement entropy, and emergent conformal symmetries, with implications for non-equilibrium phase transitions.

Contribution

It establishes a link between the heating phase Hamiltonian and the Modular Hamiltonian, and explores the holographic duals and algebraic transitions in Floquet CFTs.

Findings

Heating phase Hamiltonian equals Modular Hamiltonian.

Boundary entanglement entropy matches Rindler entropy.

Operator algebra transitions from type I to type III_1.

Abstract

In this article, we explore the connection between the heating phase of periodically driven CFTs and the Modular Hamiltonian of a subregion in the vacuum state. We show that the heating phase Hamiltonian corresponds to the Modular Hamiltonian, with the fixed points mapping to the endpoints of the subregion. In the bulk dual, we find that these fixed points correspond to the Ryu-Takayanagi surface of the AdS-Rindler wedge. Consequently, the entanglement entropy associated to the boundary interval within two fixed points exactly matches with the Rindler entropy of AdS-Rindler. We observe the emergent Virasoro algebra in the boundary quantization of the Modular Hamiltonian has a striking similarity with the emergent near Horizon Virasoro algebra. This is a consequence of the fact that while obtaining the boundary Virasoro algebra, a cut-off with conformal boundary condition around the fixed point is introduced, which in the bulk is related to a stretched horizon, with an emergent two-dimensional conformal symmetry. We also argue that as one tunes the parameter space of Floquet Hamiltonians to transition from the non-heating to the heating phase the operator algebra type changes from Von Neumann type $I$ to $III_1$ factor, providing a non-equilibrium analogue of the Hawking-Page transition.