TY - JOUR

T1 - Anomalous bulk behavior in the free parafermion Z(N) spin chain

AU - Alcaraz, Francisco C.

AU - Batchelor, Murray T.

N1 - Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/6/8

Y1 - 2018/6/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85048472583&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.97.062118

DO - 10.1103/PhysRevE.97.062118

M3 - Article

SN - 2470-0045

VL - 97

JO - Physical Review E

JF - Physical Review E

IS - 6

M1 - 062118

ER -