We describe the critical behavior of 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 (P) and time-reversal (T ) operations. The dynamic Mott transition is identified as a PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken 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.Non-Hermitian PT -symmetric quantum Hamiltonian models introduced in the seminal work of Bender and Boettcher [1] offer a foundation for the description of non-equilibrium steady states of dissipative quantum systems [2][3][4][5]. The basic property of non-Hermitian PTsymmetric models is that their eigenstates exhibit a continuous PT symmetry-breaking phase transition when the strength of the external non-conservative driving force exceeds a certain threshold value. Below this threshold, i.e. in the regime of unbroken PT symmetry, the energy eigenvalues are real, while above it the energy spectrum acquires an imaginary part. In this Letter we demonstrate that the imaginary part of a PTsymmetric Hamiltonian arises from the combined effects of the driving field and inherent dissipation. This offers a perfect framework for the theoretical description of out-of-equilibrium open quantum systems and dynamic transitions that occur in them.PT -symmetric models arise across the entire nonequilibrium physics and describe optical waveguides [6], electric RLC circuits [7], microwave cavities [8] and superconducting wires [9], to name a few. Here we focus on a theory of electric field or current driven Mott metal-insulator transitions (MIT) as a PT symmetrybreaking phenomenon. The interest in non-equilibrium MIT is motivated by both the intellectual appeal of understanding dynamic instabilities in quantum manybody strongly correlated systems and the high technological promise of Mott systems as a platform for switching devices in emergent electronics [10]. There have been tantalizing reports of field-driven Mott MIT in VO 2 [11,12], La 2−x Sr x NiO 4 [13], one-dimensional Mott insulators Sr 2 CuO 3 /SrCuO 2 [14], and organic compounds [15], yet the critical behavior at the dynamic Mott transition remained unexplored. In a recent experimental breakthrough [16], the current-driven Mott transition has been observed in a system of vortices pinned by a periodic array of proximity coupled superconduct-ing islands. Notably, the revealed critical behavior of the dynamic resistance near the dynamic Mott critical point appeared to belong to the liquid-gas transition universality class. Here we propose the PT sym...

The cleanest way to observe a dynamic Mott insulator-to-metal transition (DMT) without the interference from disorder and other effects inherent to electronic and atomic systems, is to employ the vortex Mott states formed by superconducting vortices in a regular array of pinning sites. Here, we report the critical behavior of the vortex system as it crosses the DMT line, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory for the DMT based on the parity reflection-time reversal (PT ) symmetry breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and hence the transition belonging in the thermal universality class. DOI: 10.1103/PhysRevB.97.020504 A Mott insulator [1][2][3] arising from the concurrent action of the electron-electron correlations and electron trapping by a periodic atomic potential is an exemplary manifestation of many-body quantum physics [4][5][6][7][8]. A remarkable correspondence between the quantum mechanics in a D-dimensional system and the classical statistical mechanics of a D + 1-dimensional system [9] leads to the conjecture about its classical counterpart, a vortex Mott insulator that would form in a type II superconductor if the density of the superconducting vortices matches the density of the pinning sites [10,11]. Experimentally, the vortex Mott insulator was claimed in the studies of the vortex matching effect in Ref. [12], and was conclusively evidenced in Ref. [13] by measurements of the compressibility of the vortex system localized by periodic surface holes. The implications of the existence of the vortex Mott state are far reaching. First and foremost, the Mottness embraces not only the quantum but classical realm, thus offering a perfect laboratory to study quantum many-body physics by exploring classical vortex systems.An enabling discovery of the current-driven vortex Mott insulator-to-metal transition in a proximity array [14] provided the first tangible example of a dynamic Mott transition having settled the vortex quantum mechanical mapping on a firm experimental basis. That the revealed nonequilibrium critical behavior with respect to the nonequilibrium drive is the same as that of a conventional thermal Mott transition with respect to temperature raises a largely open class of questions. Among these is a central issue in condensed matter physics: the generalization of a thermodynamic phase transition to nonequilibrium conditions. There have been tantalizing reports that in systems where tuning parameters such as temperature, pressure, or magnetic field alter the symmetry, the nonequilibrium drive generates an effective temperature an...

We study the issues of scaling and universality in spectral and transport properties of the infinite dimensional particle-hole symmetric (halffilled) Hubbard model within dynamical mean field theory. One of the simplest and extensively used impurity solvers, namely the iterated perturbation theory approach is reformulated to avoid problems such as analytic continuation of Matsubara frequency quantities or calculating multidimensional integrals, while taking full account of the very sharp structures in the Green's functions that arise close to the Mott transitions and in the Mott insulator regime. We demonstrate its viability for the half-filled Hubbard model. Previous known results are reproduced within the present approach. The universal behavior of the spectral functions in the Fermi liquid regime is emphasized, and adiabatic continuity to the non-interacting limit is demonstrated. The dc resistivity in the metallic regime is known to be a non-monotonic function of temperature with a 'coherence peak'. This feature is shown to be a universal feature occurring at a temperature roughly equal to the low energy scale of the system. A comparison to pressure dependent dc resistivity experiments on Selenium doped NiS2 yields qualitatively good agreement. Resistivity hysteresis across the Mott transition is shown to be described qualitatively within the present framework. A direct comparison of the thermal hysteresis observed in V2O3 with our theoretical results yields a value of the hopping integral, which we find to be in the range estimated through first-principle methods. Finally, a systematic study of optical conductivity is carried out and the changes in absorption as a result of varying interaction strength and temperature are identified.

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