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arXiv:2108.05760 · Physical review. B./Physical review. B

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

Lea Lenke, Matthias Mühlhauser, Kai Phillip Schmidt

Published Nov 19, 2021• 21 citations
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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.

DOI
10.1103/physrevb.104.195137

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Effective non-Hermitian physics for degenerate ground states of a non-Hermitian Ising model with RT\mathcal{RT}RT symmetry
In this paper, based on a one-dimensional non-Hermitian spin model with -invariant term, we study the non-Hermitian physics for the two (nearly) degenerate ground states. By using the high-order perturbation method, an effective pseudo-spin model is obtained to describe non-Hermitian physics for the two (nearly) degenerate ground states, which are precisely consistent with the numerical calculations. We found that there may exist effective (anti) symmetry for the effective pseudo-spin model of the two (nearly) degenerate ground states. In particular, there exists spontaneous (anti) -symmetry breaking for the topological degenerate ground states with tunable parameters in external fields. We also found that even a very tiny imaginary external field applied will drive phase transition.
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