mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 19:53:45 +01:00
46 lines
1.1 KiB
Plaintext
46 lines
1.1 KiB
Plaintext
|
op_with_no_indices = 1*C^+() + 1*C() + -1*C^+()C()
|
||
|
|
op_with_many_indices = 1*C^+(3,15,b,0,-5) + 1*C(1,2,a,1,-2)
|
||
|
|
|
||
|
|
Anticommutators:
|
||
|
|
{1*C^+(1), 1*C(1)} = 1
|
||
|
|
{1*C^+(1), 1*C(2)} = 0
|
||
|
|
{1*C^+(1), 1*C(3)} = 0
|
||
|
|
{1*C^+(2), 1*C(1)} = 0
|
||
|
|
{1*C^+(2), 1*C(2)} = 1
|
||
|
|
{1*C^+(2), 1*C(3)} = 0
|
||
|
|
{1*C^+(3), 1*C(1)} = 0
|
||
|
|
{1*C^+(3), 1*C(2)} = 0
|
||
|
|
{1*C^+(3), 1*C(3)} = 1
|
||
|
|
|
||
|
|
Commutators:
|
||
|
|
[1*C^+(1), 1*C(1)] = -1 + 2*C^+(1)C(1)
|
||
|
|
[1*C^+(1), 1*C(2)] = 2*C^+(1)C(2)
|
||
|
|
[1*C^+(1), 1*C(3)] = 2*C^+(1)C(3)
|
||
|
|
[1*C^+(2), 1*C(1)] = 2*C^+(2)C(1)
|
||
|
|
[1*C^+(2), 1*C(2)] = -1 + 2*C^+(2)C(2)
|
||
|
|
[1*C^+(2), 1*C(3)] = 2*C^+(2)C(3)
|
||
|
|
[1*C^+(3), 1*C(1)] = 2*C^+(3)C(1)
|
||
|
|
[1*C^+(3), 1*C(2)] = 2*C^+(3)C(2)
|
||
|
|
[1*C^+(3), 1*C(3)] = -1 + 2*C^+(3)C(3)
|
||
|
|
|
||
|
|
Algebra:
|
||
|
|
x = 1*C(0)
|
||
|
|
y = 1*C^+(1)
|
||
|
|
-x = -1*C(0)
|
||
|
|
x + 2.0 = 2 + 1*C(0)
|
||
|
|
2.0 + x = 2 + 1*C(0)
|
||
|
|
x - 2.0 = -2 + 1*C(0)
|
||
|
|
2.0 - x = 2 + -1*C(0)
|
||
|
|
3.0*y = 3*C^+(1)
|
||
|
|
y*3.0 = 3*C^+(1)
|
||
|
|
x + y = 1*C^+(1) + 1*C(0)
|
||
|
|
x - y = -1*C^+(1) + 1*C(0)
|
||
|
|
(x + y)*(x - y) = 2*C^+(1)C(0)
|
||
|
|
|
||
|
|
N^3:
|
||
|
|
N = 1*C^+(dn)C(dn) + 1*C^+(up)C(up)
|
||
|
|
N^3 = 1*C^+(dn)C(dn) + 1*C^+(up)C(up) + 6*C^+(dn)C^+(up)C(up)C(dn)
|
||
|
|
New N^3 = 1*C^+(dn)C(dn) + 1*C^+(up)C(up) + 6*C^+(dn)C^+(up)C(up)C(dn)
|
||
|
|
X = -1*C^+(1)C^+(2)C(4)C(3)
|
||
|
|
dagger(X) = -1*C^+(3)C^+(4)C(2)C(1)
|