High-order series expansion of non-Hermitian quantum spin models
- URL: http://arxiv.org/abs/2108.05760v1
- Date: Thu, 12 Aug 2021 14:06:40 GMT
- Title: High-order series expansion of non-Hermitian quantum spin models
- Authors: L. Lenke, M. M\"uhlhauser, K.P. Schmidt
- Abstract summary: We investigate the low-energy physics of non-Hermitian quantum spin models with $PT$-symmetry.
We consider the one-dimensional Ising chain and the two-dimensional toric code in a non-Hermitian staggered field.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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