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Journal of Jiangsu University of Science and Technology

Asymmetric Hubbard Model and Mott Metal-Insulator Transition

Wang Qi-fang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Starting from the standard Hubbard model, this paper obtained an asymmetric Hamiltonian for the half-filled strongly correlated system by ignoring the jumping of electrons with spin-σ between lattice sites when the motion of electrons with spin σ is considered. The mean field approximation is applied to get the quasi-particle spectrum of the Hamiltonian. The results at zero-temperature and finite temperature are analyzed,the possibility and critical temperature of Mott metal-insulator transition is also investigated.

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Starting from the standard Hubbard model, this paper obtained an asymmetric Hamiltonian for the half-filled strongly correlated system by ignoring the jumping of electrons with spin-σ between lattice sites when the motion of electrons with spin σ is considered. The mean field approximation is applied to get the quasi-particle spectrum of the Hamiltonian. The results at zero-temperature and finite temperature are analyzed,the possibility and critical temperature of Mott metal-insulator transition is also investigated.
We investigate the Mott metal-insulator transition in the asymmetric Hubbard model, which may describe the ground states of fermionic atoms trapped in optical lattices. We use the dynamical mean-field theory and the equation of motion approach to calculate the density of states at the Fermi level and the double occupation for various values of the on-site interaction U and the hopping asymmetry r . The critical interaction is also obtained as a function of the hopping asymmetry. Our results are in good agreement with the ones obtained by using the dynamical mean field theory with the exact diagonalization and the quantum Monte Carlo techniques.
Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or 1+x1+x1+x the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction Uc{U}_{c}Uc​ at which the metal-insulator transition occurs.
Mott metal-insulator transitions in an M-fold orbitally degenerate Hubbard model are studied by means of a generalization of the linearized dynamical mean-field theory. The method allows for an efficient and reliable determination of the critical interaction Uc{U}_{\mathrm{c}}Uc​ for any integer filling n and different M at zero temperature. For half filling a linear dependence of Uc{U}_{\mathrm{c}}Uc​ on M is found. Inclusion of the (full) Hund's rule exchange J results in a strong reduction of Uc.{U}_{\mathrm{c}}.Uc​. The transition turns out to change qualitatively from continuous for J=0J=0J=0 to discontinuous for any finite J. This result is confirmed using the exact-diagonalization method for M=2.M=2.M=2.