Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory

TL;DR

This paper investigates the entanglement entropy in the non-unitary Lee-Yang quantum field theory, computing twist field form factors and analyzing the entropy's scaling and corrections, revealing distinct features from unitary models.

Contribution

It introduces a method to compute entanglement entropy in non-unitary integrable models using twist field form factors and compares results with conformal field theory predictions.

Findings

Entanglement entropy scales with effective central charge as log of region size.

Form factor expansion matches conformal field theory predictions.

Next-to-leading order corrections are highly model-dependent in non-unitary theories.

Abstract

In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee-Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized) yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by $\frac{c_{\text{eff}}}{3}\log \ell$ where $c_{\text{eff}}$ is the effective central charge of the theory (a positive number related to the central charge) and $\ell$ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum), it appears to be much more model-dependent for non-unitary models.