Correlation Length and Unusual Corrections to the Entanglement Entropy

TL;DR

This paper analytically investigates corrections to the entanglement entropy in a massive lattice model, revealing how finite size and mass effects lead to deviations from simple scaling, especially in the XYZ spin chain.

Contribution

It provides an analytical expression for the Renyi entropy of the XYZ chain, highlighting novel subleading terms due to stable bound states and finite lattice effects.

Findings

Finite size and mass effects produce different correction exponents.

Correlation length behavior matches that of a bulk Ising model.

Subleading entropy terms depend on the phase-space path and are linked to bound states.

Abstract

We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Renyi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by a c=1 Conformal Field Theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path-dependent in phase-space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain.