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.

An Interpolating Ansatz for the Ground State of the Spinless Fermion Hamiltonian in D=1 and 2

1997 ◽  
Vol 11 (13) ◽  
pp. 1545-1563
Author(s):  
Miguel A. Martín-Delgado ◽  
Germán Sierra
Keyword(s):  
Critical Point ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Quantum Phase Transitions ◽  
Hartree Fock ◽  
Spinless Fermion ◽  
A Value ◽  
Bifurcation Phenomena ◽  
Half Filling

We propose an interpolating ansatz between the strong coupling and weak coupling regimes of a system of spinless interacting fermions in 1D and 2D lattices at half-filling. We address relevant issues such as the existence of Long Range Order, quantum phase transitions and the evaluation of ground state energy. In 1D our method is capable of unveiling the existence of a critical point in the coupling constant at (t/U) c =0.7483 as in fact occurs in the exact solution at a value of 0.5. In our approach this phase transition is described as an example of Bifurcation Phenomena in the variational computation of the ground state energy. In 2D the van Hove singularity plays an essential role in changing the asymptotic behaviour of the system for large values of t/U. In particular, the staggered magnetization for large t/U does not display the Hartree–Fock law [Formula: see text] but instead we find the law [Formula: see text]. Moreover, the system does not exhibit bifurcation phenomena and thus we do not find a critical point separating a CDW state from a fermion "liquid" state.

scholarly journals Ground State Energy of the Low Density Hubbard Model

2008 ◽  
Vol 131 (6) ◽  
pp. 1139-1154 ◽  
Author(s):  
Robert Seiringer ◽  
Jun Yin
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Low Density

EFFECTS OF THE NEXT-NEAREST-NEIGHBOR HOPPING IN OPTICAL LATTICES

2008 ◽  
Vol 22 (01) ◽  
pp. 33-44 ◽  
Author(s):  
YUN'E GAO ◽  
FUXIANG HAN
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
Optical Lattices ◽  
State Energy ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Dispersion Relations ◽  
Insulating Phase

Introducing the next-nearest-neighbor hopping t′ into the Bose–Hubbard model, we study its effects on the phase diagram, on the ground-state energy, and on the quasiparticle and quasihole dispersion relations of the Mott insulating phase in optical lattices. We have found that a negative value of t′ enlarges the Mott-insulating region on the phase diagram, while a positive value of t′ acts oppositely. We have also found that the effects of t′ are dependent on the dimensionality of optical lattices with its effects largest in three-dimensional optical lattices.

Ground-state energy of the Hubbard model at half filling

1996 ◽  
Vol 54 (3) ◽  
pp. 1637-1644 ◽  
Author(s):  
G. Polatsek ◽  
K. W. Becker
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Half Filling

On the Ground State of H-

1981 ◽  
Vol 36 (7) ◽  
pp. 782
Author(s):  
Uday Vanu Das Gupta ◽  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Oscillator Strength ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Expectation Values ◽  
Hartree Fock ◽  
Present Procedure

Abstract A simple and effective method is described to calculate the ground state energy of H~ starting with the Hartree Fock wavefunction. The expectation values of the opera­ tors 〈r1 • r2〉, 〈r1n + r2n〉 and 〈p1 • p2〉 can be estimated easily with the present procedure. Oscillator strength sums S(k) for k= -1,0, 1 are also evaluated.

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