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

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 ≥ 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 behavior is a topological effect.