Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions

TL;DR

This paper investigates the spectral properties of non-Hermitian quantum spin chains with boundary terms, revealing boundary-induced phase transitions and conformal invariance in the spectrum, with implications for reaction-diffusion systems.

Contribution

It provides numerical and analytical analysis of the spectrum of non-Hermitian XXZ chains with boundary terms, uncovering boundary-induced phase transitions and conformal invariance.

Findings

The energy gap relates to the inverse of the temporal correlation length.

The antiferromagnetic chain exhibits a conformal invariant spectrum.

A toy model confirms analytical results with free fermions.

Abstract

The spectrum of the non-hermitian asymmetric XXZ-chain with additional non-diagonal boundary terms is studied. The lowest lying eigenvalues are determined numerically. For the ferromagnetic and completely asymmetric chain that corresponds to a reaction-diffusion model with input and outflow of particles the smallest energy gap which corresponds directly to the inverse of the temporal correlation length shows the same properties as the spatial correlation length of the stationary state. For the antiferromagnetic chain with both boundary terms, we find a conformal invariant spectrum where the partition function corresponds to the one of a Coulomb gas with only magnetic charges shifted by a purely imaginary and a lattice-length dependent constant. Similar results are obtained by studying a toy model that can be diagonalized analytically in terms of free fermions.