The Ground-State Energy of Anisotropie Spin-Spin Interaction in One-Dimensional Chain

1969 ◽  
Vol 24 (5) ◽  
pp. 762-767
Author(s):  
A. D. Jannussis
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Ground State Energy ◽  
Ground State ◽  
Algebraic System ◽  
State Energy ◽  
Spin Interaction ◽  
Dimensional Chain ◽  
Linear Algebraic System ◽  
One Dimensional

Abstract In the present work the integral equation of Yang and Yang is studied by the method of moments. In general the solution of the integral equation is reducible to a linear algebraic system which can be solved only approximately. From the solution of the system the ground-state energy and the magnetization of the anisotropic spin-spin interaction in a one-dimensional chain is de­termined.

scholarly journals Ground-state energy of a Richardson-Gaudin integrable BCS model

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yibing Shen ◽  
Phillip Isaac ◽  
Jon Links
Keyword(s):  
Integral Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Continuum Limit ◽  
State Energy ◽  
Mean Field ◽  
Bcs Model ◽  
Energy Expression ◽  
The Continuum

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

scholarly journals Sample-size dependence of the ground-state energy in a one-dimensional localization problem

1996 ◽  
Vol 54 (1) ◽  
pp. 231-242 ◽  
Author(s):  
C. Monthus ◽  
G. Oshanin ◽  
A. Comtet ◽  
S. F. Burlatsky
Keyword(s):  
Sample Size ◽  
Ground State Energy ◽  
Ground State ◽  
Size Dependence ◽  
State Energy ◽  
Localization Problem ◽  
One Dimensional
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