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arXiv:1606.04580 · Physical Review Letters

Thermodynamics versus Local Density Fluctuations in the Metal–Mott-Insulator Crossover

J. H. Drewes, Eugenio Cocchi, Luke A. Miller, C. F. Chan, Daniel Pertot, Ferdinand Brennecke, Michael Köhl

Published Sep 20, 2016• 26 citations
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Abstract

The crossover between a metal and a Mott insulator leads to a localization of fermions from delocalized Bloch states to localized states. We experimentally study this crossover using fermionic atoms in an optical lattice by measuring thermodynamic and local (on-site) density correlations. In the metallic phase at incommensurable filling we observe the violation of the local fluctuation-dissipation theorem indicating that the thermodynamics of the system cannot be characterized by local observables alone. In contrast, in the Mott insulator we observe the convergence of local and thermodynamic fluctuations indicating the absence of long-range density-density correlations.

DOI
10.1103/physrevlett.117.135301

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We study distinctive features of local Mott insulator of trapped Bose-Fermi mixture systems on an optical lattice by using Monte-Carlo simulations of one-dimensional Bose-Fermi-Hubbard model. It was found that each species of the bosons and the fermions in a Mott insulator state had a finite stiffness but the density correlation function exhibited a quasi-long-range-order. This strongly suggested that in actual experiments the bosons and fermions of a commensurate filling with the lattice sites would form a Mott insulator state under strong interatomic interactions and have an order in their positional configuration.
Strongly correlated fermions in a crystal or in an optical lattice in the presence of binary-alloy disorder are investigated. We employ the statistical dynamical mean-field theory, which incorporates both fluctuations due to disorder and local correlations due to interaction, to solve the Anderson-Hubbard model. Localization due to disorder is studied by means of the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram consisting of disordered correlated metal, Anderson-Mott insulator, and band insulator.
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.