The Hubbard model in the strong coupling theory at arbitrary filling
TLDR
In this paper, the electron Green's function of the two-dimensional Hubbard model, derived using the strong coupling diagram technique, is self-consistently solved for different electron concentrations $n$ and tight-binding dispersions.Abstract:
Equations for the electron Green's function of the two-dimensional Hubbard model, derived using the strong coupling diagram technique, are self-consistently solved for different electron concentrations $n$ and tight-binding dispersions. Comparison of spectral functions calculated for the ratio of Hubbard repulsion to the nearest neighbor hopping $U/t=8$ with Monte Carlo data shows not only qualitative, but in some cases quantitative agreement in position of maxima. General spectral shapes, their evolution with momentum and filling in the wide range $0.7\lesssim n\leq 1$ are also similar. At half-filling and for the next nearest neighbor hopping constant $t'=-0.3t$ the Mott transition occurs at $U_c\approx 7\Delta/8$, where $\Delta$ is the initial bandwidth. This value is close to those obtained in the cases of the semi-elliptical density of states and for $t'=0$. In the case $U=8t$ and $t'=-0.3t$ the Mott gap reaches maximum width at $n=1.04$, and it is larger than that at $t'=0$ for half-filling. In all considered cases positions of spectral maxima are close to those in the Hubbard-I approximation.read more
Citations
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The Hubbard model in strong magnetic field: Low-frequency quantum oscillations due to strong electron correlations
TL;DR: In this article, the density of states at the Fermi level as a function of the inverse magnetic induction was calculated using the strong coupling diagram technique, and the frequency of these oscillations increased by an order of magnitude with the change of the deviation from half-filling from small to moderate values.
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The Hubbard model: exact constraints on spectral moments in the strong coupling limit
TL;DR: In this article , exact spectral moment relations are derived and presented for the low temperature, strong coupling limit of the Hubbard model, for any dimension, lattice structure and electron density, and the results generate an exact, rigorous and quantitative test for proposed solutions to the Hubbard Model that claim to be valid in the strong coupling, low temperature region.
References
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