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.
We study the differential resistivity transition of two-dimensional superconducting arrays induced by an external driving current, in the presence of thermal fluctuations and a magnetic field corresponding to
f flux quantum per plaquette. Recent experiments have identified this transition as a dynamic vortex Mott insulator transition at vortex densities near rational values of
f. The critical behavior is determined from a scaling analysis of the current-voltage relation near the transition, obtained by Monte Carlo simulations of a Josephson-junction array model in the vortex representation. For a square-lattice array, the critical exponents obtained near
f=1/2 are consistent with the experimental observations. The same scaling behavior is observed near
f=1/3. For a honeycomb array, although similar results are obtained for
f=1/3, the transition is absent for
f=1/2, consistent with an incommensurate vortex phase.
We study the dynamic vortex Mott transition in two-dimensional superconducting arrays in a magnetic field with
f flux quantum per plaquette. The transition is induced by external driving current and thermal fluctuations near rational vortex densities set by the value of
f and has been observed experimentally from the scaling behavior of the differential resistivity. Recently, numerical simulations of interacting vortex models have demonstrated this behavior only near fractional
f. A fine-grid vortex model is introduced, which allows us to consider both the cases of fractional and integer
f. The critical behavior is determined from a scaling analysis of the current-voltage relation and voltage correlations near the transition and by Monte Carlo simulations. The critical exponents for the transition near
f=1/2 are consistent with the experimental observations and previous numerical results from a standard vortex model. The same scaling behavior is obtained for
f=1, in agreement with experiments. However, the estimated correlation-length exponent indicates that even at integer
f, the critical behavior is not of mean-field type.
We study electric transport near the Mott metal-insulator transition in a triangular-lattice Hubbard model at half filling. We calculate optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ based on a cellular dynamical mean-field theory including vertex corrections inside the cluster. Near the Mott critical end point, a Drude analysis in the metallic region suggests that the change in the Drude weight is important rather than that in the transport scattering rate for the Mott transition. In the insulating region, there emerges an ``in-gap'' peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ at low $\ensuremath{\omega}$ near the Mott transition, and this smoothly connects to the Drude peak in the metallic region with decreasing Coulomb repulsion. We find that the weight of these peaks exhibits a power-law behavior upon controlling Coulomb repulsion at the critical temperature. The obtained critical exponent suggests that conductivity does not correspond to magnetization or energy density of the Ising universality class in contrast to several previous works.
Finding microscopic models for metallic states that exhibit quantum critical properties is a major theoretical challenge. We calculate the dynamical local spin susceptibility $\ensuremath{\chi}(T,\ensuremath{\omega})$ for a Hubbard model at half-filling using dynamical mean-field theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite-temperature critical point. The signature of the latter is $\ensuremath{\omega}/T$ scaling, where $\ensuremath{\omega}$ is the frequency and
T is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity, and they are relevant to experiments on organic charge-transfer salts.
We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a nonperfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi-one-dimensional model displays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be $\ensuremath{\nu}\ensuremath{\approx}1.0$. This implies that the fermionic Mott transition belongs to the universality class of the 2D Ising model.