Symmetry Resolved Entanglement Entropy: Equipartition under Driven and Non-unitary Evolution in a Compact Boson CFT

TL;DR

This paper investigates how symmetry-resolved entanglement entropy evolves in driven Floquet CFTs, revealing conditions under which charge sector equipartition breaks down due to mode coupling, with implications for non-unitary dynamics.

Contribution

It introduces a parameter controlling equipartition breakdown in symmetry-resolved entropies within Floquet CFTs, linked to an $rak{sl}^{(k)}(2,b R)$ subalgebra, and extends the analysis to non-unitary evolution.

Findings

Symmetry-resolved entropies approach or depart from equipartition depending on mode coupling.

The $rak{sl}^{(k)}(2,b R)$ subalgebra parameter influences equipartition breakdown.

Non-unitary evolution modifies the real-time dynamics of symmetry-resolved entropies.

Abstract

We study the evolution of symmetry-resolved entanglement entropy in bulk-driven Floquet conformal field theories (CFTs). Focusing on the two-dimensional free compact boson CFT, we analyze how symmetry-resolved R\'enyi entropies approach or depart from equipartition among charge sectors. We show that the existence of an $\mathfrak{sl}^{(k)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra introduces a free parameter, the label $k$, which allows us to control the breakdown of equipartition. We argue that this effect originates from an explicit coupling between low- and high-frequency modes. Based on a general oscillator representation of the Virasoro algebra, we expect this mechanism to persist beyond the free boson CFT. Finally, we discuss how the real-time dynamics of fine-grained symmetry-resolved entropies of a boundary state are modified under non-unitary evolution, which can be associated with post-selected weak measurements.