scholarly journals Mean-field theory for Bose-Hubbard model under a magnetic field

2007 ◽  
Vol 75 (4) ◽  
Author(s):  
M. Ö. Oktel ◽  
M. Niţă ◽  
B. Tanatar
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Hubbard Model ◽  
Mean Field Theory ◽  
Mean Field

COMPREHENSIVE MEAN FIELD THEORY FOR THE HUBBARD MODEL

1992 ◽  
Vol 06 (05n06) ◽  
pp. 731-747 ◽  
Author(s):  
V. JANIŠ ◽  
D. VOLLHARDT
Keyword(s):  
Field Theory ◽  
Energy Transfer ◽  
Hubbard Model ◽  
Entire Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Exact Expression ◽  
Grand Potential ◽  
Input Parameters

We derive an exact expression for the grand potential of the Hubbard model in d=∞ dimensions. By simplifying the energy transfer between up and down spins we obtain a comprehensive mean-field theory for this model. It is (i) thermodynamically consistent in the entire range of input parameters, (ii) conserving and, (iii) exact in several non-trivial limits, e. g. in the free (U→0), atomic (t→0) and Heisenberg (U≫t, n=1) limit.

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