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

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Many-Body Physics

Background:

• Understanding interacting fermion systems is crucial in condensed matter physics.
• Non-Hermitian physics introduces unique phenomena not found in Hermitian systems.
• Spin-orbit coupling significantly influences electron behavior in low-dimensional materials.

Purpose of the Study:

• To investigate the emergence of many-body resonance in a 1D spin-1/2 interacting fermion system.
• To analyze the interplay between interaction and non-Hermitian spin-orbit coupling.
• To characterize the resulting thermodynamic distribution and phase transitions.

Main Methods:

• Development of an explicit Bethe-ansatz wave function.
• Factorization of the wave function into Slater determinants and a Jastrow factor in the dilute limit.
• Construction of an effective thermodynamic distribution using an effective Hamiltonian.

Main Results:

• Observation of a many-body resonance driven by interaction and non-Hermitian spin-orbit coupling.
• Identification of an effective Hamiltonian incorporating Pauli exclusion repulsion and a resonance-induced zigzag potential.
• Demonstration of a phase transition from uniform distribution to phase separation.
• Clustering of particles with identical spins in the phase-separated state.

Conclusions:

• The many-body resonance significantly alters the system's behavior, leading to phase separation.
• Repulsive interactions enhance the many-body resonance effect, promoting particle clustering.
• The study provides insights into novel quantum phenomena in non-Hermitian interacting systems.