High-order series expansion of non-Hermitian quantum spin models

Lenke L, Mühlhauser M, Schmidt KP (2021)


Publication Type: Journal article

Publication year: 2021

Journal

Book Volume: 104

Article Number: 195137

Journal Issue: 19

DOI: 10.1103/PhysRevB.104.195137

Abstract

We investigate the low-energy physics of non-Hermitian quantum spin models with PT symmetry. To this end, we consider the one-dimensional Ising chain and the two-dimensional toric code in a non-Hermitian staggered field. For both systems, dual descriptions in terms of non-Hermitian staggered Ising interactions in a conventional transverse field exist. We perform high-order series expansions about the high- and low-field limit for both systems to determine the ground-state energy per site and the one-particle gap. The one-dimensional non-Hermitian Ising chain is known to be exactly solvable. Its ground-state phase diagram consists of second-order quantum phase transitions, which can be characterized by logarithmic singularities of the second derivative of the ground-state energy and, in the symmetry-broken phase, the gap closing of the low-field gap. In contrast, the gap closing from the high-field phase is not accessible perturbatively due to the complex energy and the occurrence of exceptional lines in the high-field gap expression. For the two-dimensional toric code in a non-Hermitian staggered field, we study the quantum robustness of the topologically ordered phase by the gap closing of the low-field gap. We find that the well-known second-order quantum phase transition of the toric code in a uniform field extends into a large portion of the non-Hermitian parameter space. However, the series expansions become unreliable for a dominant anti-Hermitian field. Interestingly, the analysis of the high-field gap reveals the potential presence of an intermediate region.

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APA:

Lenke, L., Mühlhauser, M., & Schmidt, K.P. (2021). High-order series expansion of non-Hermitian quantum spin models. Physical Review B, 104(19). https://dx.doi.org/10.1103/PhysRevB.104.195137

MLA:

Lenke, Lea, Matthias Mühlhauser, and Kai Phillip Schmidt. "High-order series expansion of non-Hermitian quantum spin models." Physical Review B 104.19 (2021).

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