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

scholarly journals Ground-state energy of a low-density Bose gas: A second-order upper bound

2008 ◽  
Vol 78 (5) ◽  
Author(s):  
László Erdős ◽  
Benjamin Schlein ◽  
Horng-Tzer Yau
Keyword(s):  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Bose Gas ◽  
Second Order ◽  
Low Density

scholarly journals Ground State Energy of the Low Density Bose Gas

1998 ◽  
Vol 80 (12) ◽  
pp. 2504-2507 ◽  
Author(s):  
Elliott H. Lieb ◽  
Jakob Yngvason
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Bose Gas ◽  
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

Ground state energy of Hubbard model

1971 ◽  
Vol 36 (2) ◽  
pp. 139-140 ◽  
Author(s):  
W.D. Langer ◽  
D.C. Mattis
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy

Ground-State Energy of a Weakly Interacting Bose Gas: Calculation Without Regularization

2004 ◽  
Vol 59 (1-2) ◽  
pp. 1-13 ◽  
Author(s):  
Christoph Weiss ◽  
Martin Block ◽  
Dave Boers ◽  
André Eckardt ◽  
Martin Holthaus
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Born Approximation ◽  
State Energy ◽  
Low Density ◽  
Density Character ◽  
Dilute Gas ◽  
Bogoliubov Approximation ◽  
Soft Interaction ◽  
Additional Device

The textbook calculation of the ground-state energy of a dilute gas of Bose particles is examined in detail, and certain mathematical inconsistencies are pointed out. On the basis of this analysis, a refined approach suitable for soft interaction potentials which lend themselves to a low-order Born approximation is developed. This procedure emphasizes the low-density character of the resulting formula for the ground-state energy, and avoids all divergent expressions at intermediate stages of the computation. It is stressed that the standard Bogoliubov approximation, if not augmented by some additional device, leads to an error which manifests itself already in the lowest order of the density. - PACS 03.75.Hh, 05.30.Jp, 03.65.Nk.

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