Curving the space by non-Hermiticity

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.

7 pages (3 figures) + 6 pages (3 figures). Added non-Hermitian realizations of quantum Hall states in curved spaces

References in corpus (6)

• Chiral Quantum Optics
• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms

Cited by in corpus (28)

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• Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch
• Hyperbolic Topological Band Insulators
• Non-Hermitian skin effect beyond the tight-binding models
• Non-Hermitian Photonic Lattices: tutorial
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Designing non-Hermitian real spectra through electrostatics
• Non-Hermitian Squeezed Polarons
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Selberg trace formula in hyperbolic band theory
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect
• Shell-Shaped Quantum Droplet in a Three-Component Ultracold Bose Gas
• Topological linear response of hyperbolic Chern insulators
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Hyperbolic Spin Liquids
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states
• Bosonic Quantum Breakdown Hubbard Model
• Entanglement between uncoupled modes with time-dependent complex frequencies
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices