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Bulletin of the American Physical Society

Influence of non-local interactions on the Mott metal-insulator transition

Malte Schüler, Erik G. C. P. van Loon, Mikhail I. Katsnelson, Tim Oliver Wehling

Published Mar 17, 2017• 0 citations
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Mott-hubbard metal-insulator transition

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Il Nuovo Cimento D•Oct 1, 1994•3 citations
A metal can be driven to an insulating phase through distinct mechanisms. A possible way is via the Coulomb interaction, which then defines the Mott metal-insulator transition (MIT). Another possibility is the MIT driven by disorder, the so-called Anderson MIT. Here we analyze interacting particles in disordered Hubbard chains---thus comprising the Mott-Anderson physics---by investigating the ground-state entanglement with density functional theory. The localization signature on entanglement is found to be a decreasing on the entanglement degree in comparison to the clean (without interaction and disorder) case, with local minima at certain critical densities. Individually, the Mott (Anderson) MIT has a single critical density whose minimum entanglement decreases as the interaction (disorder) enhances. While in the Mott MIT entanglement saturates at finite values, characterizing partial localization, in the Anderson MIT the system reaches full localization, with zero entanglement, for sufficiently strong disorder. In the combined Mott-Anderson MIT, we find three critical densities referring to local minima on entanglement. One of them is the same as for the Anderson MIT, but now the presence of interaction requires a stronger disorder potential to induce full localization. A second critical density is related to the Mott MIT, but due to disorder it is displaced by a factor proportional to the concentration of impurities. The third local minimum on entanglement is unique to the concomitant presence of disorder and interaction, found to be related to an effective density phenomenon, thus referred to as a Mott-like MIT. Since entanglement has been intrinsically connected to the magnetic susceptibility---a quantity promptly available in cold-atom experiments---our detailed numerical description might be useful for the experimental investigation of the Mott-Anderson MIT.
Metal-insulator transitions are studied within a three-component Falicov-Kimball model, which mimics a mixture of one-component and two-component fermionic particles with local repulsive interactions in optical lattices. Within the model, the two-component fermionic particles are able to hop in the lattice, while the one-component fermionic particles are localized. The model is studied by using the dynamical mean-field theory with exact diagonalization. Its homogeneous solutions establish Mott transitions for both commensurate and incommensurate fillings between one-third and two-thirds. At commensurate one-third and two-thirds fillings, the Mott transition occurs for any density of hopping particles, while at incommensurate fillings, the Mott transition can occur only for density one-half of hopping particles. At half-filling, depending on the repulsive interactions, the reentrant effect of the Mott insulator is observed. As increasing local interaction of hopping particles, the first insulator-metal transition is continuous, whereas the second metal-insulator transition is discontinuous. The second metal-insulator transition crosses a finite region where both metallic and insulating phase coexist. At third-filling, the Mott transition is established only for strong repulsive interactions. A phase separation occurs together with the phase transition.
We introduce a Cellular Dynamical Cluster Approximation (CDCA) to study the nature of the Mott insulator-metal transition in the extended Hubbard model on a square lattice. At strong coupling, a d-wave Mott insulator is obtained. Hole doping drives a first order Mott transition to a non-Fermi (nFL) liquid metal. Remarkably, this nFL is caused by an Anderson orthogonality catastrophe at low energies due to the non-trivial competition between strong, non-local interactions and hopping. This constitutes the first explicit realisation of Anderson's Luttinger liquid idea in two dimensions. Many experimental responses in the ``strange metal'' phase found around optimal doping in cuprates are understood naturally within our approach.