Symmetry-Resolved Entanglement Entropy from Heat Kernels

TL;DR

This paper introduces a comprehensive heat kernel-based method for calculating symmetry-resolved entanglement entropy in charged quantum systems, addressing limitations of previous formulas and extending applicability across dimensions.

Contribution

It develops a globally convergent heat kernel expansion that unifies charged and neutral entanglement entropy calculations, applicable to various spacetime dimensions and states.

Findings

Exact agreement with (1+1)D CFT predictions.

Consistency with holographic entropy calculations.

Extension to arbitrary spacetime dimensions.

Abstract

We develop a systematic framework for computing symmetry-resolved entanglement entropies (SREE) in charged quantum systems based on an improved heat kernel approach. Although the conventional Sommerfeld formula proves effective for neutral systems, it encounters limitations when gauge fields or chemical potentials are introduced due to incomplete residue prescriptions and violations of asymptotic boundary conditions. By reconstructing the analytic structure of the heat kernel using a phase factor, we derive a globally convergent expansion that reconciles discrete residue summations with continuous spectral decompositions. We further apply this framework to Gaussian continuous multi-scale entanglement renormalization ansatz (cMERA) states and show that the entanglement entropy (EE) can be expressed in terms of the cMERA flow functions. In particular, we obtain a symmetry-resolved entanglement entropy flow equation in the presence of a chemical potential. This formulation extends naturally to arbitrary spacetime dimensions and recovers established results for neutral systems in the mu -> 0 limit. We validate our framework through two settings: (1) exact agreement with (1+1)-dimensional conformal field theory (CFT) predictions using twist-operator techniques, and (2) consistency with holographic entropy calculations on S1 x H^(d-1) geometries. Our results both unify the treatment of charged and neutral entanglement entropy and extend this treatment to real-space renormalization frameworks, providing a robust tool for probing symmetry-resolved entanglement in conformal field theories, their holographic duals, and cMERA representations.