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https://github.com/triqs/dft_tools
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39 lines
1.1 KiB
Plaintext
39 lines
1.1 KiB
Plaintext
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Anticommutators:
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{ 1*C^+(1,0) , 1*C(1,0) } = 1
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{ 1*C^+(1,0) , 1*C(2,0) } = 0
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{ 1*C^+(1,0) , 1*C(3,0) } = 0
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{ 1*C^+(2,0) , 1*C(1,0) } = 0
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{ 1*C^+(2,0) , 1*C(2,0) } = 1
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{ 1*C^+(2,0) , 1*C(3,0) } = 0
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{ 1*C^+(3,0) , 1*C(1,0) } = 0
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{ 1*C^+(3,0) , 1*C(2,0) } = 0
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{ 1*C^+(3,0) , 1*C(3,0) } = 1
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Commutators:
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[ 1*C^+(1,0) , 1*C(1,0) ] = -1 + 2*C^+(1,0)C(1,0)
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[ 1*C^+(1,0) , 1*C(2,0) ] = 2*C^+(1,0)C(2,0)
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[ 1*C^+(1,0) , 1*C(3,0) ] = 2*C^+(1,0)C(3,0)
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[ 1*C^+(2,0) , 1*C(1,0) ] = 2*C^+(2,0)C(1,0)
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[ 1*C^+(2,0) , 1*C(2,0) ] = -1 + 2*C^+(2,0)C(2,0)
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[ 1*C^+(2,0) , 1*C(3,0) ] = 2*C^+(2,0)C(3,0)
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[ 1*C^+(3,0) , 1*C(1,0) ] = 2*C^+(3,0)C(1,0)
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[ 1*C^+(3,0) , 1*C(2,0) ] = 2*C^+(3,0)C(2,0)
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[ 1*C^+(3,0) , 1*C(3,0) ] = -1 + 2*C^+(3,0)C(3,0)
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Algebra:
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x = 1*C(0,0)
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y = 1*C^+(1,0)
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-x = -1*C(0,0)
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x + 2.0 = 2 + 1*C(0,0)
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2.0 + x = 2 + 1*C(0,0)
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x - 2.0 = -2 + 1*C(0,0)
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2.0 - x = 2 + -1*C(0,0)
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3.0*y = 3*C^+(1,0)
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y*3.0 = 3*C^+(1,0)
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x + y = 1*C^+(1,0) + 1*C(0,0)
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x - y = -1*C^+(1,0) + 1*C(0,0)
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(x + y)*(x - y) = 2*C^+(1,0)C(0,0)
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N^3:
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N = 1*C^+(0,dn)C(0,dn) + 1*C^+(0,up)C(0,up)
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N^3 = 1*C^+(0,dn)C(0,dn) + 1*C^+(0,up)C(0,up) + 6*C^+(0,dn)C^+(0,up)C(0,up)C(0,dn)
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