Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space

Abstract

Non-Hermitian systems in condensed matter Physics are well studied in recent years. In conventional viewpoint, the non-Hermiticity of a Hamiltonian is obtained by dissipative or gain and loss. Recently, some people investigate the non-Hermiticity from other perspective, which point out that non-Hermiticity may come from the curved space. In this letter, we derive a duality between a generalized non-Hermitian HN model in $d$-dimensional flat space and a Hermitian system in $3d$-dimensional curved space, and give the metric of the curved space analytically. From this duality, we establish a correspondence between Hermitian and non-Hermitian systems, which gives a new perspective to explore non-Hermitian systems.

References in corpus (22)

• Edge states and topological invariants of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Second-Order Topological Phases in Non-Hermitian Systems
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Higher-order non-Hermitian skin effect
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Second-order topological non-Hermitian skin effects
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Non-Hermitian second-order skin and topological modes
• Jones polynomial and knot transitions in topological semimetals
• Topological Field Theory of Non-Hermitian Systems
• Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems
• Curving the space by non-Hermiticity

Cited by in corpus (3)

• Topological Non-Hermitian skin effect
• Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect