Entanglement Entropy from Corner Transfer Matrix in Forrester Baxter non-unitary RSOS models

TL;DR

This paper calculates bipartite entanglement entropy in non-unitary RSOS models near criticality using Corner Transfer Matrix, revealing a logarithmic scaling with correlation length and novel subleading corrections related to conformal dimensions.

Contribution

It introduces a method to compute entanglement entropy in non-unitary models and identifies the scaling behavior and corrections near criticality.

Findings

Entanglement entropy scales logarithmically with correlation length near criticality.

Subleading corrections involve fractional powers of correlation length and conformal dimension differences.

Results support the effective central charge's role in non-unitary model entanglement scaling.

Abstract

Using a Corner Transfer Matrix approach, we compute the bipartite entanglement R\'enyi entropy in the off-critical perturbations of non-unitary conformal minimal models realised by lattice spin chains Hamiltonians related to the Forrester Baxter RSOS models in regime III. This allows to show on a set of explicit examples that the R\'enyi entropies for non-unitary theories rescale near criticality as the logarithm of the correlation length with a coefficient proportional to the effective central charge. This complements a similar result, recently established for the size rescaling at the critical point, showing the expected agreement of the two behaviours. We also compute the first subleading unusual correction to the scaling behaviour, showing that it is expressible in terms of expansions of various fractional powers of the correlation length, related to the differences $\Delta-\Delta_{\min}$ between the conformal dimensions of fields in the theory and the minimal conformal dimension. Finally, a few observations on the limit leading to the off-critical logarithmic minimal models of Pearce and Seaton are put forward.