Program
Notation
For Hubbard Operator:
1 site: an integer; 4 local states: Empty, Up, Down, Filled
Xop
ex.
Xop( 1, Empty, Up )
Xop a( 2, Down, Filled );
XProd
ex.
XProd b = Xop( 3, Up, Down ) * Xop( 3,
Down, Up );
b.simplify();
XSum
ex.
XSum d = 1.5 * Xop( 4, Empty, Up ) + b
* a;
d.simplify();
For Fermion Operator:
1 site: an integer; 2 local states: Up, Down
C
ex.
C( 1, Up )
C( 2, Up ) * C( 1, Down) + C( 2,
Down )
Cdag
ex.
Cdag( 2, Up )
Cdag( 1, Down ) * C(
2, Up ) - C( 3, Down ) * Cdag( 2, Down )
For Spin Operator:
1 site: an integer
Sz
ex.
Sz( 1 )
Sz( 1 ) * Sz( 2 )
Splus
ex.
Splus( 2 )
Splus( 2 ) * Sz( 2 )
Sminus
ex.
Sminus( 1 )
Sminus( 1 ) * Sz( 1 ) - Sz( 1 )
* Sminus( 1 )
For the details of these notations, please go to Program
instruction.