Moran, N. and Pellegrino, D. and Slingerland, Joost and Kells, G. (2017) Parafermionic clock models and quantum resonance. Physical Review B, 95 (235127). ISSN 1098-0121

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Abstract

We explore the ZN parafermionic clock-model generalizations of the p-wave Majorana wire model. In particular, we examine whether zero-mode operators analogous to Majorana zero modes can be found in these models when one introduces chiral parameters to break time reversal symmetry. The existence of such zero modes implies N-fold degeneracies throughout the energy spectrum. We address the question directly through these degeneracies by characterizing the entire energy spectrum using perturbation theory and exact diagonalization. We find that when N is prime, and the length L of the wire is finite, the spectrum exhibits degeneracies up to a splitting that decays exponentially with system size, for generic values of the chiral parameters. However, at particular parameter values (resonance points), band crossings appear in the unperturbed spectrum that typically result in a splitting of the degeneracy at finite order. We find strong evidence that these preclude the existence of strong zero modes for generic values of the chiral parameters. In particular we show that in the thermodynamic limit, the resonance points become dense in the chiral parameter space. When N is not prime, the situation is qualitatively different, and degeneracies in the energy spectrum are split at finite order in perturbation theory for generic parameter values, even when the length of the wire L is finite. Exceptions to these general findings can occur at special “antiresonant” points. Here the evidence points to the existence of strong zero modes and, in the case of the achiral point of the N=4 model, we are able to construct these modes exactly.

Item Type:	Article
Keywords:	Anyons; Topological phases of matter; Quantum wires; Approximation methods for many-body systems; Exact diagonalization; Perturbation theory;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10532
Identification Number:	https://doi.org/10.1103/PhysRevB.95.235127
Depositing User:	Dr. Joost Slingerland
Date Deposited:	21 Feb 2019 12:01
Journal or Publication Title:	Physical Review B
Publisher:	American Physical Society
Refereed:	Yes
URI:	https://journals.aps.org/prb/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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