Anomalous bulk behaviour in the free parafermion $Z(N)$ spin chain

TL;DR

This paper investigates how boundary conditions drastically influence the bulk properties of a non-Hermitian $Z(N)$ spin chain model, revealing anomalous behaviors potentially linked to topological effects.

Contribution

It demonstrates that boundary conditions significantly alter bulk properties in a non-Hermitian $Z(N)$ model, highlighting boundary-dependent phenomena in parafermionic systems.

Findings

Bulk properties differ with boundary conditions for $N eq 2$

Finite-size corrections depend on boundary conditions

Anomalous bulk behavior may be topological in origin

Abstract

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple $Z(N)$ model for $N \ge 3$ for which the model hamiltonian is non-hermitian. For $N=2$ the model reduces to the well known quantum Ising model in a transverse field. For open boundary conditions the $Z(N)$ model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing $N$. Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent and the specific heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behaviour is a topological effect.