We describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity $\left(\mathcal{P}\right)$ and time-reversal $\left(\mathcal{T}\right)$ operations. The dynamic Mott transition is identified as a $\mathcal{PT}$ symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken $\mathcal{PT}$ symmetry with a real energy spectrum. We establish that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdown and describe the resulting critical behavior of transport characteristics. The obtained critical exponent is in an excellent agreement with experimental findings.

• Received 4 November 2015
• Revised 13 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.041104