Curving the space by non-Hermiticity

TL;DR

This paper reveals a duality between non-Hermitian quantum models in flat spaces and Hermitian models in curved spaces, explaining non-Hermitian phenomena through geometric principles and enabling new experimental approaches.

Contribution

It introduces a novel duality linking non-Hermitian and Hermitian models via space curvature, offering a geometric understanding of non-Hermitian phenomena.

Findings

Non-Hermitian effects can be explained by dual models in curved spaces.

Prototypical 1D chains are equivalent to duals in 2D hyperbolic spaces.

Non-uniform tunnelings can tailor local space curvatures.

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.