Diagram technique for the Hubbard model

Vladimir, M. I.; Moskalenko, V. A.

doi:10.1007/bf01029224

Cited by 95 publications

(153 citation statements)

References 10 publications

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“…Notice that in this approximation K does not depend on momentum. Now we need to calculate the cumulants in equation (10). To do this it is convenient to introduce the Hubbard operators X (5) can be computed straightforwardly:…”

Section: Diagram Techniquementioning

confidence: 99%

“…However, the use of the interpolation overrates somewhat values of |ℑK(ω)| which leads to the overestimation of the tails in the real part. To correct this defect the interpolated K(ω) is scaled so that in the far tails its real part coincides with the values obtained from equation (10).…”

Section: Spectral Functionmentioning

confidence: 99%

“…As indicated in [ 8,10,13], if K(k, iω l ) is approximated by this cumulant the result corresponds to the Hubbard-I approximation [ 2].…”

Section: Diagram Techniquementioning

confidence: 99%

“…Besides, these rules and the graphical representation of the expansion vary depending on the choice of the operator precedence. The diagram technique suggested in references [ 10,11,12,13] is free from these defects. In this approach the power expansion for Green's function of electron operators a nσ and a † nσ is considered and the terms of the expansion are expressed as site cumulants of these operators.…”

Section: Introductionmentioning

confidence: 99%

“…In this approach the power expansion for Green's function of electron operators a nσ and a † nσ is considered and the terms of the expansion are expressed as site cumulants of these operators. Based on this diagram technique the equations of the Larkin type [ 15] for Green's function were derived [ 10,12,13].…”

Section: Introductionmentioning

confidence: 99%

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Evolution of the spectrum of the Hubbard model with filling

Sherman¹

2006

Condens. Matter Phys.

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The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion. The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators. For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions and nearest-neighbor hopping. With decreasing the electron concentration in addition to the four bands observed at half-filling a narrow band arises near the Fermi level. The dispersion of the new band, its bandwidth and the variation with filling are close to those of the spin-polaron band in the t-J model.

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Section: Diagram Techniquementioning

confidence: 99%

Section: Spectral Functionmentioning

confidence: 99%

“…As indicated in [ 8,10,13], if K(k, iω l ) is approximated by this cumulant the result corresponds to the Hubbard-I approximation [ 2].…”

Section: Diagram Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evolution of the spectrum of the Hubbard model with filling

Sherman¹

2006

Condens. Matter Phys.

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The Hubbard model in the strong coupling theory at arbitrary filling

Sherman

2015

Physica Status Solidi (b)

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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

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Strong-Coupling Diagram Technique for Strong Electron Correlations

Sherman

2016

Nanomaterials for Security

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Diagram technique for the Hubbard model

Cited by 95 publications

References 10 publications

Evolution of the spectrum of the Hubbard model with filling

Evolution of the spectrum of the Hubbard model with filling

The Hubbard model in the strong coupling theory at arbitrary filling

Strong-Coupling Diagram Technique for Strong Electron Correlations

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