Alcaraz, Francisco C.Batchelor, Murray2020-06-152020-06-151063-651Xhttp://hdl.handle.net/1885/205032We 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.The work of FCA is supported in part by the Brazilian agencies FAPESP and CNPq. The work of MTB is supported by The 1000 Talent Program of China, National Natural Science Foundation of China Grant No. 11574405, and Australian Research Council Discovery Project DP180101040.application/pdfen-AU©2018 American Physical Society201810.1103/PhysRevE.97.0621182019-12-22