Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.
We consider the orthogonality catastrophe at the Anderson metal-insulator transition (AMIT). The typical overlap
F between the ground state of a Fermi liquid and the one of the same system with an added potential impurity is found to decay at the AMIT exponentially with system size
L as $F\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}c{L}^{\ensuremath{\eta}})$, where $\ensuremath{\eta}$ is the power of multifractal intensity correlations. Thus, strong disorder typically increases the sensitivity of a system to an added impurity exponentially. We recover, on the metallic side of the transition, Anderson's result that the fidelity
F decays with a power law $F\ensuremath{\sim}{L}^{\ensuremath{-}q({E}_{F})}$ with system size
L. Its power increases as the Fermi energy
EF approaches the mobility edge
EM as $q({E}_{F})\ensuremath{\sim}[({E}_{F}\ensuremath{-}{E}_{M})/{E}_{M}{]}^{\ensuremath{-}\ensuremath{\nu}\ensuremath{\eta}}$, where $\ensuremath{\nu}$ is the critical exponent of the correlation length ${\ensuremath{\xi}}_{c}$. On the insulating side of the transition,
F is constant for system sizes exceeding the localization length $\ensuremath{\xi}$. While these results are obtained for the typical fidelity
F, we find that
logF is widely, log normally, distributed with a width diverging at the AMIT. As a consequence, the mean value of the fidelity
F converges to one at the AMIT, in strong contrast to its typical value which converges to zero exponentially fast with system size
L. This counterintuitive behavior is explained as a manifestation of multifractality at the AMIT.
We study the effects of an orbital magnetic field on the Mott metal-insulator transition in the Hubbard-Hofstadter model. We demonstrate that sufficiently large magnetic fields induce a Mott insulator-to-metal phase transition supporting our claim with dynamical mean field theory (DMFT) numerical results. For both competing phases (metal and insulator) we observe a magnetic-field-induced metallization reflected in an enhancement of kinetic and potential energy. The kinetic energy of the Mott insulator increases due to the Aharonov-Bohm effect experienced by electrons virtually tunneling around an elementary plaquette which is, however, suppressed by strong correlations. The kinetic energy of the metallic phase, on the other hand, is more strongly affected by the magnetic field through a field-driven redistribution of spectral weight due to the formation of magnetic minibands. This leads to an increase of the kinetic energy which tends to stabilize the metallic state. Our theoretical results might be relevant for recent experimental studies on magnetic field driven insulator-to-metal transitions in strongly correlated materials such as VO_{2}, λ-type organic conductors, and moiré multilayers.