The Hubbard model in the strong coupling theory at arbitrary filling

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.Comment: 10 pages, 6 figures. arXiv admin note: text overlap with arXiv:1410.828

Continuum of many-particle states near the metal-insulator transition in the Hubbard model

“…Here a metallic state occurs by a gradual closure of the Mott gap as the temperature increases. This behavior resembles that found in lower-order approximation [24,25,26]. Finally, Fig.…”

“…As a whole shapes and locations of maxima in spectra in Fig. 2 are similar to those obtained in lower-order approximation [25,26] and by cluster approaches [37,38,39]. Figures 3 and 4 correspond to two qualitatively different metallic solutions, which have finite spectral intensities on the Fermi level.…”

“…As was shown in [13,14,24,25,26], K(kj) approximated by the sum of diagrams (a) and (b) in Fig. 1 allows one to describe the MIT and to obtain spectral functions in reasonable agreement with Monte Carlo results for T t. In this approximation the irreducible part is local, K(l ′ τ ′ , lτ ) ∝ δ l ′ l , and, therefore, its Fourier transform is independent of k. The diagrams (c) and (d) correspond to local terms and, therefore, they are supposed not to introduce qualitative changes into the solutions obtained earlier.…”

“…In this approximation the MIT is the second-order transition. Besides, the approximation was shown [25,26] to give spectral functions in reasonable agreement with high-temperature results of Monte Carlo simulations for a number of parameters and electron concentrations.…”

“…The derived equations for the electron Green's function were solved by iteration for moderate values of the Hubbard repulsion U and temperature, as well as for different values of η in the starting Green's function obtained from the Hubbard-I approximation. For the local K constructed from lower-order terms a similar procedure gave solutions, which were independent of η [25,26]. We found that the inclusion of the nonlocal term leads to a dependence of obtained solutions on η, that manifests itself mainly near the Fermi level -widths of the Mott gap in insulating solutions and shapes of spectral functions in a vicinity of the Fermi level in metallic solutions are changed as η varies in some range.…”