Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain

TL;DR

This paper investigates the Renyi entanglement entropy in the 1D XYZ spin-1/2 chain, revealing essential singularities at non-conformal critical points and proposing entropy as a tool to distinguish phase transition types.

Contribution

It uncovers essential singularities in the entropy at non-conformal critical points and links entropy behavior to the nature of phase transitions in the XYZ chain.

Findings

Entropy scales logarithmically near conformal points.

Essential singularity in entropy at non-conformal points.

Discontinuous transition characterized by level crossing.

Abstract

We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.