Far-from-equilibrium dynamics in open fermion chains

Recent attention has been paid to the study of open systems coupled to Markovian reservoirs using MPS techniques.

One such system, the spinless fermion t-V model on the chain, equivalent to the spin XXZ model, has been extensively studied both numerically and analytically. It showcases ballistic, diffusive and insulating behavior depending on the interaction and driving strength.

Earlier results for the spin model on a ladder indicate that the ballistic regime appears to be absent. This model is however fundamentally different from the fermion version, due to non-trivial string operators that arise as a result of the Jordan-Wigner transformation, which renders earlier conclusions inapplicable.


In addition to the MPS based methods we use a Gaussian steady state approach to study the mentioned models as a more efficient way of exploring the phase diagram. Additionally this allows us to determine which mean field decouplings play a more important role paving the way for the development of a field theory for the out of equilibrium ballistic-diffusive-insulating transition. We also explore the differences between the fermion and spin ladder, in particular showing that the former can exhibit ballistic behavior.