Entanglement Entropy from the Truncated Conformal Space

TL;DR

This paper introduces a numerical method based on the truncated conformal spectrum approach to compute Renyi entanglement entropies in one-dimensional quantum field theories, effectively capturing the transition from massless to massive regimes.

Contribution

It extends the truncated conformal spectrum approach to calculate entanglement entropies, applicable to both ground and excited states, and demonstrates its effectiveness in various deformations of free fermions.

Findings

Reproduces the known crossover function for massive free fermions.

Accurately captures the massless to massive transition in small systems.

Successfully computes Renyi entropies for low-lying excited states.

Abstract

A new numerical approach to entanglement entropies of the Renyi type is proposed for one-dimensional quantum field theories. The method extends the truncated conformal spectrum approach and we will demonstrate that it is especially suited to study the crossover from massless to massive behavior when the subsystem size is comparable to the correlation length. We apply it to different deformations of massless free fermions, corresponding to the scaling limit of the Ising model in transverse and longitudinal fields. For massive free fermions the exactly known crossover function is reproduced already in very small system sizes. The new method treats ground states and excited states on the same footing, and the applicability for excited states is illustrated by reproducing Renyi entropies of low-lying states in the transverse field Ising model.