Entanglement entropy of non-unitary integrable quantum field theory

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 c eff 3 log where c eff is the effective central charge of the theory (a positive number related to the central charge) and 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.

Entanglement entropies of minimal models from null-vectors

“…The problem of entanglement entropy in non-unitary models has already been addressed in various contexts [33,[39][40][41]. For comparison with the existing literature on the subject, we clarify in this section the specific choices and observations that we made for non-unitary models.…”

Entanglement entropy and boundary renormalization group flow: Exact results in the Ising universality class

“…The OPEs of the twist fields with other fields 53 have been extensively explored in many circumstances [35][36][37]39,54 , but nevertheless remain elusive in general. The bosonization procedure which is known for orbifolds of free theories 41 , as applied here in the context of entanglement, leads to a number of applications.…”

Distinguishing Black Hole Microstates using Holevo Information

“…Similar to what we have done for the contributions to the Holevo information from the vacuum conformal family, we can use the OPE of twist operators [7,[16][17][18][19][20][21][22][23][24], and get the leading contributions from a non-identity primary operator ψ, (27) in the main text.…”

“…To get the short and long interval Holevo information χ A and χ B , we need to calculate the short and long interval EEs of thermal state, i.e., S A , S B , and the average of the short interval EEs of the microstates, i.e., i p i S A,i . For the short interval, as in [12][13][14][15], we use the operator product expansion (OPE) of twist operators [7,[16][17][18][19][20][21] to calculate the short interval expansion of the EE. This method is still available for the long interval case [22][23][24].…”