Nonequilibrium thermal state of a voltage-biased Mott insulator

We establish the nonequilibrium thermal phases of a voltage driven antiferromagnetic Mott insulator in three dimensions, realised at steady state under a voltage bias. Starting from the Keldysh action for the half filled Hubbard model we derive an effective Langevin equation for the `slow' magnetic variables. The coupling of electrons to these degrees of freedom determine the transport properties. At low temperature we find a voltage-driven discontinuous insulator-metal transition, along with hysteresis. We map the suppression of the N\'eel temperature $T_N$ and pseudogap temperature $T_{pg}$ with increasing voltage, and discover that the biased Mott insulator has a finite temperature insulator-metal transition. The low temperature results resolve an experimental puzzle about hysteresis, and the thermal results make testable predictions on spectra and nonlinear transport.