Curving the space by non-Hermiticity

Chenwei Lv, Ren Zhang, Zhengzheng Zhai and Qi Zhou ()
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Chenwei Lv: Purdue University
Ren Zhang: Purdue University
Zhengzheng Zhai: Purdue University
Qi Zhou: Purdue University

Nature Communications, 2022, vol. 13, issue 1, 1-6

Abstract: 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 to engineer curvatures or implementing synthetic curved spaces to explore non-Hermitian quantum physics.

Date: 2022
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DOI: 10.1038/s41467-022-29774-8

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