We study the electronic state of the doped Mott-Hubbard insulator within the dynamical mean field theory. The evolution of the finite temperature spectral functions as a function of doping show large redistributions of spectral weight in both antiferromagnetic and paramagnetic phases. In particular, a metallic antiferromagnetic state is obtained with a low frequency Slater-splitted quasiparticle peak coexisting with Hubbard bands. In the high temperature paramagnetic metallic phase, upon reducing doping, the system has a crossover through a ``bad metal'' state characterized by an anomalous shift of the quasiparticle peak away from the Fermi energy. We find that the charge compressibility of the antiferromagnetic metal is dramatically enhanced upon approaching the second order N\'eel line.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.
A powerful diagrammatic impurity solver is shown to permit a systematic study of the doping-driven Mott transition in a one-band Hubbard model within the framework of single-site dynamical mean-field theory. At small dopings and large interaction strengths, we are able to access low enough temperatures that a reliable extrapolation to temperature
T=0 may be performed, and ground state energies of insulating and metallic states may be compared. We find that the
T=0 doping-driven transition is of second order and is characterized by an interaction-strength dependent electronic compressibility, which vanishes at the critical interaction strength of the half filled model. Over wide parameter ranges, the compressibility is substantially reduced relative to the noninteracting system. The metal-insulator transition is characterized by the appearance of in-gap states, but these are relevant only for very low dopings of less than 3%.
For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength
U, temperature
T, and filling
n shows that, upon increasing
n toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T
= 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.
Filling-control metal-insulator transition on the two-dimensional Hubbard model is investigated by using the correlator projection method, which takes into account momentum dependence of the free energy beyond the dynamical mean-field theory. The phase diagram of metals and Mott insulators is analyzed. Lifshitz transitions occur simultaneously with metal-insulator transitions at large Coulomb repulsion. On the other hand, they are separated each other for lower Coulomb repulsion, where the phase sandwiched by the Lifshitz and metal-insulator transitions appears to show violation of the Luttinger sum rule. Through the metal-insulator transition, quasiparticles retain nonzero renormalization factor and finite quasi-particle weight in the both sides of the transition. This supports that the metal-insulator transition is caused not by the vanishing renormalization factor but by the relative shift of the Fermi level into the Mott gap away from the quasiparticle band, in sharp contrast with the original dynamical mean-field theory. Charge compressibility diverges at the critical end point of the first-order Lifshitz transition at finite temperatures. The origin of the divergence is ascribed to singular momentum dependence of the quasiparticle dispersion.
We investigate the local moment formation in the half-filled
SU(N) Hubbard model under a staggered ionic potential. As the Hubbard
U increases, the charge fluctuations are suppressed and eventually frozen when
U is above a critical value
Uc, marking the development of well-defined local moment with integer
m fermions on the A sublattice and $(N\ensuremath{-}m)$ fermions on the B sublattice, respectively. We obtain an analytical solution for
Uc for the paramagnetic ground state within the variational Gutzwiller approximation and renormalized mean field theory. For large
N,
Uc is found to depend on
N linearly with fixed
m/N, but sublinearly with fixed
m. The local moment formation is accompanied by a peculiar phase transition from the band insulator to the Mott insulator, where the ionic potential and quasiparticle weight are renormalized to zero simultaneously. Inside the Mott phase, the low-energy physics is described by the
SU(N) Heisenberg model with conjugate representations, which is widely studied in the literature.