Charged moments and symmetry-resolved entanglement from Ballistic Fluctuation Theory

TL;DR

This paper applies Ballistic Fluctuation Theory to study charged moments and symmetry-resolved entanglement in quantum many-body systems, deriving analytic expressions for various states and confirming quasiparticle conjectures.

Contribution

It extends the application of Ballistic Fluctuation Theory to composite twist fields and provides explicit formulas for charged Re9nyi entropies in free fermion systems.

Findings

Analytic expressions for charged Re9nyi entropies at equilibrium and out of equilibrium.

Results agree with quasiparticle picture predictions.

Extension of BFT to composite twist fields with gauge fields.

Abstract

The charged moments of a reduced density matrix provide a natural starting point for deriving symmetry-resolved R\'enyi and entanglement entropies, which quantify how entanglement is distributed among symmetry sectors in the presence of a global internal symmetry in a quantum many-body system. In this work, we study charged moments within the framework of Ballistic Fluctuation Theory (BFT). This theory describes large-scale ballistic fluctuations of conserved charges and associated currents and, by exploiting the height-field formulation of twist fields, gives access to the asymptotic behaviour of their two-point correlation functions. In Del Vecchio Del Vecchio et al. $[1]$, this approach was applied to the special case of branch-point twist fields used to compute entanglement entropies within the replica approach. Here, we extend those results by applying BFT to composite branch-point twist fields, obtained by inserting an additional gauge field. Focusing on free fermions, we derive analytic expressions for charged R\'enyi entropies both at equilibrium, in generalized Gibbs ensembles, and out of equilibrium following a quantum quench from $U(1)$ preserving pair producing integrable initial states. In the latter case, our results agree with the conjecture arising from the quasiparticle picture.