Exact Analysis of a One-Dimensional Yang-Gaudin Model with Two-Body Loss

TL;DR

This paper demonstrates that the one-dimensional Yang-Gaudin model with two-body loss remains exactly solvable, revealing how dissipation influences spin configuration stability in many-body quantum systems.

Contribution

It provides an exact analysis of the Yang-Gaudin model with dissipation, relating the Liouvillian spectrum to a non-Hermitian Hamiltonian and exploring dissipation effects on spin states.

Findings

Exact solution for the two-body problem with dissipation.

Steady-state solutions exist in the bosonic singlet sector.

Dissipation reverses spin stability preferences in many-body systems.

Abstract

We show that the one-dimensional Yang-Gaudin model with two-body loss remains exactly solvable irrespective of whether constituent particles are bosons or fermions. By relating the Liouvillian spectrum to the right eigenvalues of a non-Hermitian effective Hamiltonian obtained by complexifying the interaction strength, we derive a general expression for the initial particle-loss rate. We then solve the two-body problem exactly and show that, in the bosonic singlet sector, the effective Hamiltonian has real right eigenvalues and the master equation admits steady-state solutions. For many-body systems with three or more particles, we further show that dissipation reverses which spin configurations are most stable: in bosonic systems it favors antiferromagnetic-like configurations over ferromagnetic-like ones, whereas in fermionic systems it favors ferromagnetic-like configurations over antiferromagnetic-like ones.