DISCUSSION ON THE MEAN FIELD APPROXIMATION IN THE RVB THEORY

1988 ◽  
Vol 02 (10) ◽  
pp. 1205-1209 ◽  
Author(s):  
R.B. TAO ◽  
X. HU ◽  
M. SUZUKI
Keyword(s):  
Hubbard Model ◽  
Strong Correlation ◽  
Magnetic System ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Hubbard Hamiltonian ◽  
Half Filling ◽  
The Mean

Baskaran’s mean field approximation of the Hubbard Hamiltonian with strong correlation and half-filling is discussed. Our calculations show that his decoupling of the Hamiltonian is not permissible in the half-filling case and that it destroys the equivalence of the Hubbard model to the Heisenberg magnetic system and violates some spin-spin relations.

scholarly journals Энергетический спектр и оптические свойства фуллерена C-=SUB=-80-=/SUB=-(I-=SUB=-h-=/SUB=-) в модели Хаббарда

2021 ◽  
Vol 129 (10) ◽  
pp. 1227
Author(s):  
А.В. Силантьев
Keyword(s):  
Group Theory ◽  
Hubbard Model ◽  
Symmetry Group ◽  
Mean Field ◽  
Analytical Form ◽  
Field Approximation ◽  
Energy Spectra ◽  
Mean Field Approximation ◽  
The Mean

The anticommutative Green’s functions were derived in an analytical form, and the energy spectra of С80 fullerene and endohedral Y3N@C80 fullerene of symmetry group Ih were obtained within the Hubbard model in the mean-field approximation. Using group theory methods, the classification of energy states was carried out, and the allowed transitions in the energy spectra of С80 and Y3N@C80 molecules of symmetry group Ih were determined.

POSSIBLE COEXISTENCE OF ANTIFERROMAGNETISM AND SUPERCONDUCTIVITY IN THE HUBBARD MODEL

1988 ◽  
Vol 01 (09n10) ◽  
pp. 341-347 ◽  
Author(s):  
SHEN JUE-LIAN ◽  
SU ZHAO-BIN ◽  
DONG JIN-MING ◽  
YU LU
Keyword(s):  
Hubbard Model ◽  
High Temperature Superconductivity ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Antiferromagnetic Order ◽  
Effective Hamiltonian ◽  
Hamiltonian Approach ◽  
Theoretical Approaches ◽  
The Mean

The Hubbard model in the nearly half-filled case was studied in the mean field approximation using the effective Hamiltonian approach. Both antiferromagnetic order parameter and condensation of singlet pairs were considered. In certain parameter range the coexistence of antiferromagnetism and superconductivity is energetically favorable. Relations to the high temperature superconductivity and other theoretical approaches are also discussed.

Mean-Field Analysis of the Three-Band Hubbard Model

1998 ◽  
Vol 12 (27n28) ◽  
pp. 2831-2845 ◽  
Author(s):  
Yabin Yu ◽  
Guanghan Cao ◽  
Zhengkuan Jiao
Keyword(s):  
Electronic Structure ◽  
Hubbard Model ◽  
Singlet State ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Mean Field Approximation ◽  
Band Model ◽  
Spin Singlet ◽  
Half Filling ◽  
The Mean

A full three-band model for the CuO 2 plane of cuprates, which includes all the essential interaction — Cu-O and O-O hopping and the Coulomb repulsion on the Cu and O sites and between them, is considered. Its antiferromagnetic ground state for the half-filling is studied by using the mean field approximation. The electronic structure and the magnetic properties such as the densities of states, the energy spectra, the composition of holes (Cu or O character), the superexchange interaction and the magnetic moment are calculated and in general, our results are in agreement with the available experimental and other calculation results. Meanwhile, we find that the influence of the O-O hopping and Cu-O intrasite Coulomb repulsion on these properties is considerable. Our estimate of the energy of the spin singlet state above the antiferromagnetic background indicates that the lowest excitation state of the holes is the singlet state and give a charge-transfer energy in agreement with the experiment. We also discuss the hole-doping to the antiferromagnetic background and find the mean field approach invalid. Finally, based on the electronic structure at the half-filling, en effective one-band Hubbard model is presented and the effective parameters are close to the values given by the computation on the clusters.

scholarly journals Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 58
Author(s):  
Zlatko Koinov
Keyword(s):  
Phase Diagram ◽  
Optical Lattices ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Recent Developments ◽  
Topological States ◽  
Half Filling ◽  
The Mean

Motivated by recent developments in the experimental study of ultracold atoms in graphene-like honeycomb optical lattices, we investigate superconductivity of the attractive Kane-Mele-Habbard (KMH) model with the next-nearest-neighbor (NNN) hoping at half filling. The mean-field approximation is used to study the phase diagram which interpolates the trivial and the non-trivial topological states. It is shown that: (a) when the NNN hoping is taken into account, one has to introduce two mean-field gap equations for the two sublattices, instead of a single gap when the NNN hopping is neglected, and (b) in the non-trivial topological region the phase diagram with the NNN hopping is significantly different compared to the phase diagram calculated previously, but without the NNN term. We also discuss the superconducting instability of the attractive KMH model that is driven by condensation of Cooperons.

scholarly journals On the Validity of the Dynamical Mean-Field Approximation for Studying the Two-Dimensional Hubbard Model on a Square Lattice

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
A. N. Ribeiro ◽  
C. A. Macedo
Keyword(s):  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Two Dimensional ◽  
Infinite Dimensions ◽  
Antiferromagnetic Correlations ◽  
Half Filling

The dynamical mean-field approximation (DMFA) becomes exact in the limit of infinite dimensions, and allows results to be obtained in a nonperturbative regime without the limitations normally found with exact diagonalization (ED) and quantum Monte Carlo (QMC) methods. In this paper, we investigate the applicability of the method to lattices with small coordination number in special situations. Specifically we use this approximation to study the two-dimensional (2D) Hubbard model on a square lattice far from half filling. In this situation, we calculate the specific heat and find that when the filling decreases, that is, antiferromagnetic correlations become less important, the agreement between DMFA and QMC results increases. Our results show that the DMFA can be a valuable technique for studying the thermodynamic properties of the Hubbard model also on a square lattice, but within a parameter range in which the antiferromagnetic correlations are not important.

scholarly journals ITINERANT AND LOCALIZED STATES IN STRONGLY CORRELATED SYSTEMS BY A MODIFIED MEAN-FIELD SLAVE-BOSON APPROACH

2001 ◽  
Vol 15 (05) ◽  
pp. 479-490 ◽  
Author(s):  
EMMANUELE CAPPELLUTI
Keyword(s):  
Hubbard Model ◽  
Mean Field ◽  
Field Approximation ◽  
Localized States ◽  
Mean Field Approximation ◽  
Strongly Correlated ◽  
Correlated Systems ◽  
The Mean ◽  
Hubbard Operators ◽  
Natural Way

The standard mean field slave-boson solution for the infinite-U Hubbard model is revised. A slightly modified version is proposed which includes properly the incoherent contribution of the localized states. In contrast to the standard mean field result, this new proposed solution defines a unique spectral function to be used in the calculation of local and not local quantities, and satisfies the correct thermodynamic relations. The same approach is applied also to the mean field approximation in terms of Hubbard operators. As a byproduct of this analysis, Luttinger's theorem is shown to be fulfilled in a natural way.

scholarly journals Энергетический спектр и оптические свойства фуллерена С-=SUB=-36-=/SUB=- в модели Хаббарда

2019 ◽  
Vol 127 (8) ◽  
pp. 191
Author(s):  
А.В. Силантьев
Keyword(s):  
Group Theory ◽  
Hubbard Model ◽  
Symmetry Group ◽  
Mean Field ◽  
Field Approximation ◽  
Energy Spectra ◽  
Mean Field Approximation ◽  
Endohedral Fullerene ◽  
The Mean ◽  
Energy States

AbstractThe anticommutator Green’s functions and the energy spectra of fullerene С_36 and endohedral fullerene La@C_36, with both of them belonging to the D _6 h symmetry group, are obtained analytically within the Hubbard model in the mean-field approximation. Using group-theory methods, their energy states are classified and allowed transitions in the energy spectra of the С_36 and La@C_36 molecules, both belonging to the D _6 h symmetry group, are determined.

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