Dynamical preparation of a steady ODLRO state in the Hubbard model with local non-Hermitian impurity

TL;DR

This paper demonstrates that a non-Hermitian impurity in the Hubbard model can dynamically generate a steady state with off-diagonal long-range order, resembling superconductivity, through a process insensitive to initial conditions and impurity placement.

Contribution

It introduces a method to produce a steady ODLRO state in a non-Hermitian Hubbard model via dynamical evolution, highlighting the role of high-order exceptional points.

Findings

Real spectrum maintained despite local non-Hermitian impurity

Generation of steady superconducting-like state from arbitrary initial states

Insensitivity to on-site interaction and impurity location

Abstract

The cooperation between non-Hermiticity and interaction brings about a lot of counterintuitive behaviors, which are impossible to exist in the framework of the Hermitian system. We study the effect of a non-Hermitian impurity on the Hubbard model in the context of $\eta $ symmetry. We show that the non-Hermitian Hubbard Hamiltonian can respect a full real spectrum even if a local non-Hermitian impurity is applied to. The balance between dissipation of single fermion and on-site pair fluctuation results in a highest-order coalescing state with off-diagonal long-range order (ODLRO). Based on the characteristic of High-order EP, the critical non-Hermitian Hubbard model allows the generation of such a steady superconducting-like state through the time evolution from an arbitrary initial state, including the vacuum state. Remarkably, this dynamic scheme is insensitive to the on-site interaction and entirely independent of the locations of particle dissipation and pair fluctuation. Our results lay the groundwork for the dynamical generation of a steady ODLRO state through the critical non-Hermitian strongly correlated system.