Duality between the generalized non-Hermitian Hatano-Nelson model in flat space and a Hermitian system in curved space

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