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