Time-dependent driving of quantum systems has emerged as a powerful tool to
engineer exotic phases far from thermal equilibrium; when the drive is periodic
this is called Floquet engineering. The presence of many-body interactions can
lead to runaway heating, so that generic systems are believed to heat up until
they reach a featureless infinite-temperature state. Finding mechanisms to slow
down or even avoid this heat death is a major goal -- one such mechanism is to
drive toward an even distribution of electrons in momentum space. Here we show
how such a mechanism avoids the heat death for a charge-density-wave chain in a
strong dc electric field; minibands with nontrivial distribution functions
develop as the current is prematurely driven to zero. We also show how the
field strength tunes between positive, negative, or close-to-infinite effective
temperatures for each miniband. These results suggest that nontrivial
metastable distribution functions should be realized in the prethermal regime
of quantum systems coupled to slow bosonic modes.Comment: 5 pages, 4 figures (plus supplemental material: 8 pages, 7 figures