$\eta $-pairing ground states in the non-Hermitian Hubbard model

TL;DR

This paper explores how non-Hermitian imaginary hoppings influence the ground states of the attractive Hubbard model, revealing a transition to $ ext{eta}$-pairing states and enriching understanding of non-Hermitian strongly correlated systems.

Contribution

It provides an exact solution showing the suppression of non-Hermiticity by electron correlations and identifies a phase transition to $ ext{eta}$-pairing ground states with increasing imaginary hopping.

Findings

Electron-electron correlation suppresses non-Hermiticity.

Existence of a transition from normal to $ ext{eta}$-pairing ground states.

Ground states exhibit off-diagonal long-range order (ODLRO).

Abstract

The introduction of non-Hermiticity has greatly enriched the research field of traditional condensed matter physics, and eventually led to a series of discoveries of exotic phenomena. We investigate the effect of non-Hermitian imaginary hoppings on the attractive Hubbard model. The exact bound-pair solution shows that the electron-electron correlation suppresses the non-Hermiticity, resulting in off-diagonal long-range order (ODLRO) ground state. In a large negative $U $ limit, the ODLRO ground state corresponds to $\eta $-spin ferromagnetic states. We also study the system with mixed hopping configuration. The numerical result indicates the existence of the transition from normal to $\eta $-pairing ground states by increasing the imaginary hopping strength. Our results provide a promising approach for the non-Hermitian strongly correlated system.