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Nuclear Physics B

Towards a microscopic theory of the metal-insulator transition

Claudio Castellani, C. Di Castro, Gabor Forgács, Eugenio Tabet

Published Nov 1, 1983• 24 citations
Publisher
DOI
10.1016/0550-3213(83)90420-0

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The Metal Insulator Transition in the Hubbard Model

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We devise a variational approach to the metal-insulator transition (MIT) that combines the Mott and Hubbard aspects of localization. Starting from the Gutzwiller approach, we optimize the ground-state energy not only with respect to the double occupancy \ensuremath{\eta}, but also with respect to the single-particle wave functions, which enter the energy via expressions for the Coulomb interaction U and for the bare bandwidth W. In effect, we obtain a theory of the MIT without resorting to a parametrization in terms of U/W. The effective mass close to the MIT is strongly enhanced even when the transition is discontinuous.
The celebrated Wiedemann-Franz (WF) law is believed to be robust in metals as long as interactions between electrons preserve their fermion-quasiparticle character. We study thermal transport and the fate of the WF law close to a continuous metal-insulator transition (MIT) in the Falicov-Kimball model (FKM) using cluster-dynamical mean-field theory (CDMFT). Surprisingly, as for electrical transport, we find robust and novel quantum critical scaling in thermal transport across the MIT. We unearth the deeper reasons for these novel findings in terms of (i) the specific structure of energy-current correlations for the FKM and (ii) the microscopic electronic processes which facilitate energy transport while simultaneously blocking charge transport close to the MIT. However, within (C)DMFT, we also find that the WF law survives at $T\ensuremath{\longrightarrow}0$ in the incoherent metal right up to the MIT, even in absence of Landau quasiparticles.
A wide range of disordered materials, including disordered correlated systems, show universal dielectric response (UDR), followed by a superlinear power-law increase in their optical responses over exceptionally broad frequency regimes. While extensively used in various contexts over the years, the microscopics underpinning UDR remains controversial. Here, we investigate the optical response of the simplest model of correlated fermions, the Falicov-Kimball model, across the continuous metal-insulator transition (MIT) and analyze the associated quantum criticality in detail using cluster extension of dynamical mean-field theory. Surprisingly, we find that UDR naturally emerges in the quantum critical region associated with the continuous MIT. We tie the emergence of these novel features to a many-body orthogonality catastrophe accompanying the onset of strongly correlated electronic glassy dynamics close to the MIT, providing a microscopic realization of Jonscher's time-honored proposal as well as a rationale for similarities in optical responses between correlated electronic matter and canonical glass formers.