Curving the space by non-Hermiticity
- URL: http://arxiv.org/abs/2106.02477v2
- Date: Thu, 30 Dec 2021 01:14:11 GMT
- Title: Curving the space by non-Hermiticity
- Authors: Chenwei Lv, Ren Zhang, Zhengzheng Zhai, Qi Zhou
- Abstract summary: We show that non-Hermitian phenomena can be naturally explained by a duality between non-Hermitian models in flat spaces and their counterparts, which could be Hermitian, in curved spaces.
Such a duality unfolds deep geometric roots of non-Hermitian phenomena, delivers an unprecedented routine connecting Hermitian and non-Hermitian physics, and gives rise to a theoretical perspective reformulating our understandings of curvatures and distance.
In practice, it provides experimentalists with a powerful two-fold application, using non-Hermiticity as a new protocol to engineer curvatures or implementing synthetic curved spaces to explore
- Score: 3.613072342189595
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum systems are often classified into Hermitian and non-Hermitian ones.
Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin
effect to the supersensitivity to boundary conditions, have been widely
explored. Whereas these intriguing phenomena have been considered peculiar to
non-Hermitian systems, we show that they can be naturally explained by a
duality between non-Hermitian models in flat spaces and their counterparts,
which could be Hermitian, in curved spaces. For instance, prototypical
one-dimensional (1D) chains with uniform chiral tunnelings are equivalent to
their duals in two-dimensional (2D) hyperbolic spaces with or without magnetic
fields, and non-uniform tunnelings could further tailor local curvatures. Such
a duality unfolds deep geometric roots of non-Hermitian phenomena, delivers an
unprecedented routine connecting Hermitian and non-Hermitian physics, and gives
rise to a theoretical perspective reformulating our understandings of
curvatures and distance. In practice, it provides experimentalists with a
powerful two-fold application, using non-Hermiticity as a new protocol to
engineer curvatures or implementing synthetic curved spaces to explore
non-Hermitian quantum physics.
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