Perturbation expansion of the ground-state energy for the one-dimensional cyclic Hubbard system in the Hückel limit

1995 ◽  
Vol 53 (5) ◽  
pp. 457-466 ◽  
Author(s):  
M. Takahashi ◽  
P. Bracken ◽  
J. Čížek ◽  
J. Paldus
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Perturbation Expansion ◽  
One Dimensional ◽  
The One

scholarly journals GROUND-STATE ENERGY OF THE ONE-DIMENSIONAL HUBBARD MODEL IN A SIMPLE SELF-CONSISTENT VERSION OF THE LADDER APPROXIMATION

1995 ◽  
Vol 09 (18) ◽  
pp. 1149-1157 ◽  
Author(s):  
F.D. BUZATU
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Consistency Condition ◽  
Ladder Approximation ◽  
Model Parameters ◽  
Simple Assumption ◽  
One Dimensional ◽  
The One

The ground-state energy of the one-dimensional Hubbard model is calculated within the ladder approximation; from the comparison with the exact results in the repulsive case, it follows that the approximation is good at low densities or small couplings. The ladder approximation can be improved by imposing a self-consistency condition; using a simple assumption, the results become close to the exact ones in a large range of the model parameters.

GENERALIZED GUTZWILLER ANSATZ FOR THE HALF-FILLED HUBBARD CHAIN

1988 ◽  
Vol 02 (05) ◽  
pp. 1021-1034 ◽  
Author(s):  
Patrik Fazekas ◽  
Karlo Penc
Keyword(s):  
Wave Function ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Occupation Number ◽  
Step Function ◽  
Spin Correlations ◽  
One Dimensional ◽  
Leading Term ◽  
The One

The well-known Gutzwiller wave function is generalized by including new variational parameters to control nearest-neighbour charge-charge, charge-spin, and spin-spin correlations. The non-magnetic state of the one-dimensional, half-filled Hubbard model is studied. Within the Gutzwiller approximation, the expression for the ground state energy can be worked out analytically. The correlation between empty and doubly occupied sites is found to play the most essential role. Minimization in the large-U limit shows that the Brinkman-Rice transition has been pushed to U → ∞, and the leading term of the ground state energy density is of order −t2/ U . In contrast to results obtained with the Gutzwiller wave function, we find that the band occupation number nk is monotonically decreasing both above and below kF. The dominant k–dependence is given by ~(t/U) cos k, in agreement with t/U–expansion results. nk has also a weak step-function component, with the discontinuity at kF vanishing as (t/U)2 in the limit U/t ≫ 1.

Ground-state energy of the one-dimensional gravitational gas

1984 ◽  
Vol 30 (6) ◽  
pp. 3319-3320 ◽  
Author(s):  
I. Andrić ◽  
V. Bardek
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
One Dimensional ◽  
The One
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