Universal corrections to the entanglement entropy in gapped quantum spin chains: a numerical study

TL;DR

This study numerically investigates entanglement entropy in gapped quantum spin chains, confirming universal corrections predicted by quantum field theory and exploring deviations near non-universal regimes.

Contribution

It provides numerical validation of universal entropy corrections in gapped spin chains based on quantum field theory predictions.

Findings

Corrections to entropy saturation are proportional to Bessel function K0(2mr).

The proportionality constant relates to the number of particle types.

Numerical results match quantum field theory predictions away from the universal region.

Abstract

We carry out a numerical study of the bi-partite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the anti-ferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the SU(2)-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behaviour of the entropy. We numerically confirm that, in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to the Bessel function K0(2mr) where m is a mass scale (the inverse correlation length) and r the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted in publications involving two of the current authors for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behaviour following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length.