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2018

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

Alcaraz, Francisco C., Batchelor, Murray T.

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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 $N$.

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

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We do not revisit the N = 2 N=2 Ising case here. See, e.g., the effect of boundary conditions on this hermitian model in G. G. Cabrera and R. Jullien, Phys. Rev. B 35
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Then

For spin chains, see e.g., C. Korff and R. Weston, J. Phys. A 40
2009
Later among the works it cites.
P. Fendley, J. Phys. A 47
2014
Later among the works it cites.
See, e.g., A. S. Jermyn, R. S. K. Mong, J. Alicea and P. Fendley, Phys. Rev. B 90
2014
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F. C. Alcaraz, Phys. Rev. B 94
2016
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For a recent review on the rich physics of parafermions, see J. Alicea and P. Fendley, Annual Review of Condensed Matter Physics 7
2016
Later among the works it cites.
F. C. Alcaraz, M. T. Batchelor and Z.-Z. Liu, J. Phys. A 50
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