Always-Real-Eigenvalued Non-Hermitian Topological Systems
- URL: http://arxiv.org/abs/2111.02701v2
- Date: Tue, 15 Mar 2022 11:23:12 GMT
- Title: Always-Real-Eigenvalued Non-Hermitian Topological Systems
- Authors: Yang Long, Haoran Xue, Baile Zhang
- Abstract summary: Non-Hermitian Hamiltonians can exhibit real energy spectra under parity-time ($PT$) symmetry.
Sufficiently strong non-Hermiticity will destroy the reality of energy spectra, a situation known as spontaneous $PT$-symmetry breaking.
Our work develops so far the only theory that can guarantee the reality of energy spectra for non-Hermitian Hamiltonians.
- Score: 4.8668411144978885
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The effect of non-Hermiticity in band topology has sparked many discussions
on non-Hermitian topological physics. It has long been known that non-Hermitian
Hamiltonians can exhibit real energy spectra under the condition of parity-time
($PT$) symmetry -- commonly implemented with balanced loss and gain -- but only
when non-Hermiticity is relatively weak. Sufficiently strong non-Hermiticity,
on the other hand, will destroy the reality of energy spectra, a situation
known as spontaneous $PT$-symmetry breaking. Here, based on non-reciprocal
coupling, we show a systematic strategy to construct non-Hermitian topological
systems exhibiting bulk and boundary energy spectra that are always real,
regardless of weak or strong non-Hermiticity. Such nonreciprocal-coupling-based
non-Hermiticity can directly drive a topological phase transition and determine
the band topology, as demonstrated in a few non-Hermitian systems from 1D to
2D. Our work develops so far the only theory that can guarantee the reality of
energy spectra for non-Hermitian Hamiltonians, and offers a new avenue to
explore non-Hermitian topological physics.
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