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

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.