Quantum frustration and magnetic ordering in a Hubbard model

1988 ◽  
Vol 153-155 ◽  
pp. 1277-1278 ◽  
Author(s):  
Marc Gabay ◽  
Sebastian Doniach ◽  
Masahiko Inui
Keyword(s):  
Hubbard Model ◽  
Magnetic Ordering

The Ground State Energy of the Hubbard Model in Hubbard's Approximation

1972 ◽  
Vol 27 (6) ◽  
pp. 889-893 ◽  
Author(s):  
Rainer Jelitto
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Magnetic Ordering ◽  
Coupling Constant ◽  
Hartree Fock ◽  
The Best Approximation ◽  
Paramagnetic Solution ◽  
Neighbour Interaction

Abstract We have calculated the ground state energy of the Hubbard model in the approximation of Hubbard's first paper1 . For the neutral model with nearest neighbour interaction the energy resulting from the selfconsistent paramagnetic solution is compared with those ones following from the (ferromagnetic) Hartree-Fock and an (antiferromagnetic) single particle theory. The energy of the latter one turns out to be the best approximation of the true ground state energy of the model for all values of the coupling constant V0 , but the energy derived from Hubbard's approximation, in spite of the absence of magnetic ordering, is a reasonable approximation at least for sufficiently large values of V0.

MAGNETIC ORDERING IN A TWO-DIMENSIONAL HUBBARD MODEL

1988 ◽  
Vol 02 (01) ◽  
pp. 505-509
Author(s):  
HUI-QUAN NIE ◽  
BAO-HUA ZHAO ◽  
KAI-YI ZHANG ◽  
K.A. Chao ◽  
R. MICNAS
Keyword(s):  
Hubbard Model ◽  
Magnetic Phase ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Magnetic Phase Diagram ◽  
Magnetic Ordering ◽  
Two Dimensional ◽  
Antiferromagnetic Ordering ◽  
Monte Carlo Investigation ◽  
Magnetic Structure Factor

We have used the fourth order perturbation expansion to construct the magnetic phase diagram of the two-dimensional Hubbard model. To the contrary of the three-dimensional case, a stable antiferromagnetic phase is found at the limit of (t/U)≃0 if the electron density n lies in the region 0.95<n<1.05. Our results for n=0.9 are compared to the recent indecisive Monte-Carlo investigation on the magnetic structure factor regarding the antiferromagnetic ordering.

scholarly journals Properties of the half-filled Hubbard model investigated by the strong coupling diagram technique

2015 ◽  
Vol 29 (14) ◽  
pp. 1550088 ◽  
Author(s):  
A. Sherman
Keyword(s):  
Hubbard Model ◽  
Strong Coupling ◽  
Magnetic Ordering ◽  
Mott Transition ◽  
Near Neighbor ◽  
Diagram Technique ◽  
Spectral Functions ◽  
Spin Correlations ◽  
Occupation Numbers ◽  
Half Filling

The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion Uc ≈ 6.96t, where t is the hopping constant. The calculated spectral functions, density of states (DOS) and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for U > Uc and for temperatures, at which magnetic ordering and spin correlations are suppressed. For U < Uc and lower temperatures the theory describes qualitatively correctly the positions and widths of spectral continua, variations of spectral shapes and occupation numbers with changing wave vector and repulsion. The locations of spectral maxima turn out to be close to the positions of δ-function peaks in the Hubbard-I approximation.

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