Thermalization with detailed-balanced two-site Lindblad dissipators

The use of two-site Lindblad dissipators to generate thermal states and study heat transport was raised to prominence by Prosen and Znidaric [J. Stat. Mech. (2009) P02035]. Here we propose a variant of this method based on detailed balance of internal levels of the two-site Hamiltonian and characterize its performance. We study the thermalization profile in the chain, the effective temperatures achieved by different single- and two-site observables, and we also investigate the decay of two-time correlations. We find that at a large enough temperature, the steady state approaches closely a thermal state, with a relative error below 1% for the inverse temperature estimated from different observables.