# Non-Hermitian description of the dynamics of inter-chain pair tunnelling

## TL;DR

This paper demonstrates that the dynamics of inter-chain pair tunnelling in a two-leg ladder can be effectively described by a non-Hermitian Hubbard model, revealing spectral singularities linked to eigenstate equivalence.

## Contribution

It establishes a connection between Hermitian and non-Hermitian models through exact two-particle solutions, highlighting the physical relevance of non-Hermitian Hubbard Hamiltonians.

## Key findings

- Eigenstate equivalence between Hermitian and non-Hermitian models
- Spectral singularities emerge in the non-Hermitian Hubbard model
- The approach applies to both Bose and Fermi systems

## Abstract

We study inter-chain pair tunnelling dynamics based on an exact two-particle solution for a two-leg ladder. We show that the Hermitian Hamiltonian shares a common two-particle eigenstate with a corresponding non-Hermitian Hubbard Hamiltonian in which the non-Hermiticity arises from an on-site interaction of imaginary strength. Our results provides that the dynamic processes of two-particle collision and across-legs tunnelling are well described by the effective non-Hermitian Hubbard Hamiltonian based on the eigenstate equivalence. We also find that any common eigenstate is always associated with the emergence of spectral singularity in the non-Hermitian Hubbard model. This result is valid for both Bose and Fermi systems and provides a clear physical implication of the non-Hermitian Hubbard model.