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Register a new userFate of the false Mott-Hubbard transition in two dimensions
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We have studied the impact of non-local electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -- irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
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We study the second order finite temperature Mott transition point in the fully frustrated Hubbard model at half filling, within Dynamical Mean Field Theory. Using quantum Monte Carlo simulations we show the existence of a finite temperature second order critical point by explicitly demonstrating the existence of a divergent susceptibility as well as by finding coexistence in the low temperature phase. We determine the location of the finite temperature Mott critical point in the (U,T) plane. Our study verifies and quantifies a scenario for the Mott transition proposed in earlier studies (Reviews of Modern Physics 68, 13, 1996) of this problem.
We study theoretically the zero temperature phase transition in two dimensions from a Fermi liquid to a paramagnetic Mott insulator with a spinon Fermi surface. We show that the approach to the bandwidth controlled Mott transition from the metallic side is accompanied by a vanishing quasiparticle residue and a diverging effective mass. The Landau parameters $F^0_s, F^0_a$ also diverge. Right at the quantum critical point there is a sharply defined `critical Fermi surface but no Landau quasiparticle. The critical point has a $Tlnfrac{1}{T}$ specific heat and a non-zero $T = 0$ resistivity. We predict an interesting {em universal resistivity jump} in the residual resistivity at the critical point as the transition is approached from the metallic side. The crossovers out of the critical region are also studied. Remarkably the initial crossover out of criticality on the metallic side is to a Marginal Fermi Liquid metal. At much lower temperatures there is a further crossover into the Landau Fermi liquid. The ratio of the two crossover scales vanishes on approaching the critical point. Similar phenomena are found in the insulating side. The filling controlled Mott transition is also studied. Implications for experiments on the layered triangular lattice organic material $kappa-(ET)_2Cu_2(CN)_3$ are discussed.
The combination of bandstructure theory in the local density approximation with dynamical mean field theory was recently successfully applied to V$_2$O$_3$ -- a material which undergoes the f amous Mott-Hubbard metal-insulator transition upon Cr doping. The aim of this sh ort paper is to emphasize two aspects of our recent results: (i) the filling of the Mott-Hubbard gap with increasing temperature, and (ii) the peculiarities of the Mott-Hubbard transition in this system which is not characterized by a diver gence of the effective mass for the $a_{1g}$-orbital.
We discuss the solution of the Mott transition problem in a fully frustrated lattice with a semicircular density of states in the limit of infinite dimensions from the point of view of a Landau free energy functional. This approach provides a simple relation between the free energy of the lattice model and that of its local description in terms of an impurity model. The character of the Mott transition in infinite dimensions, (as reviewed by Georges Kotliar Krauth and Rozenberg, RMP 68, 1996, 13) follows simply from the form of the free energy functional and the physics of quantum impurity models. At zero temperature, below a critical value of the interaction U, a Mott insulator with a finite gap in the one particle spectrum, becomes unstable to the formation of a narrow band near the Fermi energy. Using the insights provided by the Landau approach we answer questions raised about the dynamical mean field solution of the Mott transition problem, and comment on its applicability to three dimensional transition metal oxides.
Identifying the fingerprints of the Mott-Hubbard metal-insulator transition may be quite elusive in correlated metallic systems if the analysis is limited to the single particle level. However, our dynamical mean-field calculations demonstrate that the situation changes completely if the frequency dependence of the two-particle vertex functions is considered: The first non-perturbative precursors of the Mott physics are unambiguously identified well inside the metallic regime by the divergence of the local Bethe-Salpeter equation in the charge channel. At low temperatures this occurs in the region where incoherent high-energy features emerge in the spectral function, while at high temperatures it is traceable up to the atomic-limit.
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