Explicit Wave Function of the Interacting Non-Hermitian Spin-1/2 1D System

We present an explicit Bethe-ansatz wave function to a 1D spin-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 wave function 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.