We consider the dimer Hubbard model within Dynamical Mean Field Theory to study the interplay and competition between Mott and Peierls physics. We describe the various metal-insulator transition lines of the phase diagram and the break down of the di
fferent solutions that occur along them. We focus on the specific issue of the debated Mott-Peierls insulator crossover and describe the systematic evolution of the electronic structure across the phase diagram. We found that at low intra-dimer hopping the emerging local magnetic moments can unbind above a characteristic singlet temperature $T^*$. Upon increasing the inter-dimer hopping subtle changes occur in the electronic structure. Notably, we find Hubbard bands of a mix character with coherent and incoherent excitations. We argue that this state is relevant for VO$_2$ and its signatures may be observed in spectroscopic studies, and possibly through pump-probe experiments.
The Mott-Anderson transition in the disordered charge-transfer model displays several new features in comparison to what is found in the disordered single-band Hubbard model, as recently demonstrated by large-scale computational (statistical dynamica
l mean field theory) studies. Here we show that a much simpler typical medium theory approach (TMT-DMFT) to the same model is able to capture most qualitative and even quantitative aspects of the phase diagram, the emergence of an intermediate electronic Griffiths phase, and the critical behavior close to the metal-insulator transition. Conceptual and mathematical simplicity of the TMT-DMFT formulation thus makes it possible to gain useful new insight into the mechanism of the Mott-Anderson transition in these models.
We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify t
he quantum critical behavior near disordered Mott transitions. The leading critical behavior of quasiparticle wavefunctions is shown to assume a universal form in the full range from weak to strong disorder, in contrast to disorder-driven non-Fermi liquid (electronic Griffiths phase) behavior, which is found only in the strongly correlated regime.
We present a large-N variational approach to describe the magnetism of insulating doped semiconductors based on a disorder-generalization of the resonating-valence-bond theory for quantum antiferromagnets. This method captures all the qualitative and
even quantitative predictions of the strong-disorder renormalization group approach over the entire experimentally relevant temperature range. Finally, by mapping the problem on a hard-sphere fluid, we could provide an essentially exact analytic solution without any adjustable parameters.
We investigate the effects of disorder within the T=0 Brinkman-Rice (BR) scenario for the Mott metal-insulator transition (MIT) in two dimensions (2d). For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanis
hing of the local quasiparticles (QP) weights Z_{i} and strong disorder screening at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of QP parameters are strongly enhanced in the critical regime, with a distribution function P(Z) ~ Z^{alpha-1} and alpha tends to zero at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the MIT, in a fashion surprisingly reminiscent of the Infinite Randomness Fixed Point scenario for disordered quantum magnets.
We present a detailed analysis of the critical behavior close to the Mott-Anderson transition. Our findings are based on a combination of numerical and analytical results obtained within the framework of Typical-Medium Theory (TMT-DMFT) - the simples
t extension of dynamical mean field theory (DMFT) capable of incorporating Anderson localization effects. By making use of previous scaling studies of Anderson impurity models close to the metal-insulator transition, we solve this problem analytically and reveal the dependence of the critical behavior on the particle-hole symmetry. Our main result is that, for sufficiently strong disorder, the Mott-Anderson transition is characterized by a precisely defined two-fluid behavior, in which only a fraction of the electrons undergo a site selective Mott localization; the rest become Anderson-localized quasiparticles.
We investigate the effects of weak to moderate disorder on the T=0 Mott metal-insulator transition in two dimensions. Our model calculations demonstrate that the electronic states close to the Fermi energy become more spatially homogeneous in the cri
tical region. Remarkably, the higher energy states show the opposite behavior: they display enhanced spatial inhomogeneity precisely in the close vicinity to the Mott transition. We suggest that such energy-resolved disorder screening is a generic property of disordered Mott systems.
Strong correlation effects, such as a dramatic increase in the effective mass of the carriers of electricity, recently observed in the low density electron gas have provided spectacular support for the existence of a sharp metal-insulator transitions
in dilute two dimensional electron gases. Here we show that strong correlations, normally expected only for narrow integer filled bands, can be effectively enhanced even far away from integer filling, due to incipient charge ordering driven by non-local Coulomb interactions. This general mechanism is illustrated by solving an extended Hubbard model using dynamical mean-field theory. Our findings account for the key aspects of the experimental phase diagram, and reconcile the early view points of Wigner and Mott. The interplay of short range charge order and local correlations should result in a three peak structure in the spectral function of the electrons which should be observable in tunneling and optical spectroscopy.
We present a theory describing the mechanism for the two-dimensional (2D) metal-insulator transition (MIT) in absence of disorder. A two-band Hubbard model is introduced, describing vacancy-interstitial pair excitations within the Wigner crystal. Kin
etic energy gained by delocalizing such excitations is found to lead to an instability of the insulator to self-doping above a critical carrier concentration $n=n_c$, mapping the problem to a density-driven Mott MIT. This mechanism provides a natural microscopic picture of several puzzling experimental features, including the large effective mass enhancement, the large resistivity drop, and the large positive magneto-resistance on the metallic side of the transition. We also present a global phase diagram for the clean 2D electron gas as a function of $n$ and parallel magnetic field $B_{shortparallel}$, which agrees well with experimental findings in ultra clean samples.
Correlation-driven screening of disorder is studied within the typical-medium dynamical mean-field theory (TMT-DMFT) of the Mott-Anderson transition. In the strongly correlated regime, the site energies epsilon_R^i characterizing the effective disord
er potential are strongly renormalized due to the phenomenon of Kondo pinning. This effect produces very strong screening when the interaction U is stronger then disorder W, but applies only to a fraction of the sites in the opposite limit (U<W).
