An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System

TL;DR

This paper introduces an explicit Bethe-ansatz wavefunction for a 1D interacting non-Hermitian spin-1/2 system, revealing a many-body resonance and phase transition driven by interaction and non-Hermitian effects.

Contribution

It provides the first explicit Bethe-ansatz wavefunction for this non-Hermitian system, demonstrating how resonance influences phase behavior and particle clustering.

Findings

Identification of a many-body resonance due to non-Hermitian spin-orbit coupling.

Observation of a phase transition from uniform distribution to phase separation.

Clustering of particles with identical spins in the resonance-enhanced phase.

Abstract

We present an explicit Bethe-ansatz wavefunction to a 1D spin-$\frac{1}{2}$ interacting fermion system, manifesting a many-body resonance resulting from the interplay between interaction and non-Hermitian spin-orbit coupling. In the dilute limit, the Bethe-ansatz wavefunction is factorized into Slater determinants and a Jastrow factor. An effective thermodynamic distribution is constructed with an effective Hamiltonian including a repulsion resulting from Pauli's exclusion principle and a distinctive zigzag potential arising from the resonance. The competition between these effects leads to a transition from a uniformly distributed configuration to a phase separation. Clustering of particles with identical spins is observed in the latter phase, demonstrating that the many-body resonance effect is enhanced by the repulsive interaction.