Field tuning to avoid the heat death of a charge-density-wave chain

Time-dependent driving of quantum systems has emerged as a powerful tool to engineer
exotic phases far from equilibrium. However, the presence of many-body interactions or the coupling to a bath inevitably leads to heating, which drives the system towards a featureless infinite-temperature state, called the heat-death of the system. Finding ways to avoid this heat death are critical for many fields that rely on implementating Floquet-state engineering. Here we show that a charge-density-wave chain placed in a strong dc electric field develops a set of minibands with nontrivial distribution functions, as the current is prematurely driven to zero. This avoids the heat-death and creates a nontrivial nonequilibrium steady state, different from equilibrium states. In particular, we see situations where the minibands appear to thermalize independently of each other, or with a weak coupling between the minibands. Depending upon whether we have resonance conditions or not, we also see the heat death and the development of negative temperature states too. This work shows that one can engineer nontrivial nonequilibrium steady states when fermions are coupled to low-energy bosons.