Phase diagram of the non-hermitean asymmetric XXZ spin chain

TL;DR

This paper analyzes the phase diagram of the asymmetric XXZ spin chain, revealing a massless conformal phase and a massive phase, with a unique scaling behavior at the phase boundary, using Bethe Ansatz methods.

Contribution

It explicitly derives low-lying excitations of the asymmetric XXZ spin chain and uncovers a novel scaling behavior at the phase transition line.

Findings

Identifies a massless conformal phase with central charge c=1

Finds a phase boundary where excitations scale as N^{-1/2}

Shows the mass gap vanishes with an exponent 1/2 near the phase transition

Abstract

The low-lying excitations of the asymmetric $XXZ$ spin chain are derived explicitly in the antiferromagnetic regime through the Bethe Ansatz. It is found that a massless and conformal invariant phase with central charge $c=1$ is separated from a massive phase by a line on which the low-lying excitations surprisingly scale with the lattice length as $\Delta E \sim N^{-\frac{1}{2}}$. The mass gap vanishes with an exponent $\frac{1}{2}$ as one approaches the massless phase. The connection with the asymmetric $6$--vertex model and some physical consequences are discussed.