Symmetry-resolved entanglement in a long-range free-fermion chain

TL;DR

This paper analyzes how long-range couplings affect the symmetry-resolved entanglement entropy in a fermionic chain, revealing differences from short-range models and providing analytical results for large subsystems.

Contribution

It extends the study of symmetry-resolved entanglement to long-range fermionic systems and derives analytical asymptotics using block Toeplitz determinants.

Findings

Entanglement equipartition holds at leading order.

Breaking of equipartition depends on long-range hopping amplitudes.

Analytical expressions for symmetry-resolved entropies are obtained.

Abstract

We investigate the symmetry resolution of entanglement in the presence of long-range couplings. To this end, we study the symmetry-resolved entanglement entropy in the ground state of a fermionic chain that has dimerised long-range hoppings with power-like decaying amplitude -- a long-range generalisation of the Su-Schrieffer-Heeger model. This is a system that preserves the number of particles. The entropy of each symmetry sector is calculated via the charged moments of the reduced density matrix. We exploit some recent results on block Toeplitz determinants generated by a discontinuous symbol to obtain analytically the asymptotic behaviour of the charged moments and of the symmetry-resolved entropies for a large subsystem. At leading order we find entanglement equipartition, but comparing with the short-range counterpart its breaking occurs at a different order and it does depend on the hopping amplitudes.