Two-parameter extended Hubbard Hamiltonian with supersymmetry

1998 ◽  
Vol 5 (3) ◽  
pp. 419-422 ◽  
Author(s):  
A. Montorsi
Keyword(s):  
Hubbard Hamiltonian ◽  
Two Parameter ◽  
Extended Hubbard Hamiltonian

Quantum Monte Carlo study of the one-dimensional extended Hubbard Hamiltonian

1991 ◽  
Vol 43 (1-2) ◽  
pp. 3531-3534 ◽  
Author(s):  
W.R Somsky ◽  
D.K Campbell ◽  
H.-Q Lin ◽  
X Wang ◽  
J.E Gubernatis
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
One Dimensional ◽  
Hubbard Hamiltonian ◽  
The One ◽  
Extended Hubbard Hamiltonian

EXTENDED HUBBARD HAMILTONIAN WITH (SUPER)SYMMETRIES: ADDITIVE POLYNOMIAL R-MATRIX FOR SOME INTEGRABLE CASES

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2953-2960 ◽  
Author(s):  
FABRIZIO DOLCINI ◽  
ARIANNA MONTORSI
Keyword(s):  
Spectral Parameter ◽  
One Dimension ◽  
Constructive Method ◽  
Permutation Operator ◽  
R Matrix ◽  
Hubbard Hamiltonian ◽  
Completely Integrable ◽  
Extended Hubbard Hamiltonian ◽  
Second Degree

We propose a constructive method to prove the integrability of a given physical Hamiltonian in one dimension, which amounts to looking for appropriate polynomial R-matrices, solutions of GYBE, whose first coefficient in the power expansion with respect to the spectral parameter is the Hamiltonian itself. The method is applied to the extended Hubbard Hamiltonian, in particular to the cases in which it exhibits so(4) or gl(2,1) symmetries. We show that in the latter case the R-matrices are at most polynomial of second degree, whose coefficients are nothing but the Hamiltonian, the identity and the permutation operator. In this way, all known completely integrable cases are recovered. Also, the method allows to recognize that the possible integrability of the most general gl(2,1) invariant Hamiltonian depends on the existence of a non-additive R-matrix.

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