Exact Bethe ansatz spectrum of a tight-binding chain with dephasing   noise
  We construct an exact map between a tight-binding model on any bipartite lattice in presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the non-equilibrium steady state and the leading decay modes describing the relaxation at late times are related to the eta-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time-evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model. 
Mariya V. Medvedyeva, Fabian H. L. Essler and Tomaz Prosen
quant-ph cond-mat.stat-mech cond-mat.str-el nlin.SI