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OperatorSetTrace
OperatorSetTrace($O$, $t$, {$i_1,...,i_n$}) takes an Operator $O$, an optional real value $t$ for the trace average and an optional list {$i_1,...,i_n$} of included orbitals, and sets the trace of these orbitals to $t$ times the number of orbitals. It furthermore sets any scalar offset of the operator to 0 (or rather will, with the next update). If no list of indices is given the function includes all orbitals up to the number of fermionic states, and if no value $t$ is given the trace is set to 0.
After the operation the operator has the property \begin{equation*} \sum_{j=\{i_1,...,i_n\}} \frac{O_{jj}}{n} = t \hspace{0.3cm} , \end{equation*} where $O_{jj}$ are the prefactors of the diagonal quadratic terms of the operator, \begin{equation*} O = \sum_{i,j} O_{ij} a_i^\dagger a_j^{\phantom{\dagger}} + ... \hspace{0.3cm} . \end{equation*}
Input
-
$O$ : Operator
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$t$ : New value of the trace average (Default 0)
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{$i_1,...,i_n$} : List of indices (Default {$0,...,N_{Fermi}-1$})
Output
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$O^\prime$ : Operator with newly set trace
Example
Input
- Example.Quanty
Orbitals = {"1s","2s"} Indices, NF = CreateAtomicIndicesDict(Orbitals) e1s = 1 e2s = 2 F0ss = 0.5 O = NewOperator("Number", NF, Indices["1s"], Indices["1s"],{e1s, e1s}) + NewOperator("Number", NF, Indices["2s"], Indices["2s"],{e2s, e2s}) + NewOperator("U", NF, Indices["1s_Up"], Indices["1s_Dn"],{F0ss}) + NewOperator("U", NF, Indices["2s_Up"], Indices["2s_Dn"],{F0ss}) O.Name = "Operator" print(O) print("Set Operator trace average to 0") OperatorSetTrace(O) print(O) print("Set Operator trace average to 2") OperatorSetTrace(O,2) print(O) print("Set trace average of 1s orbitals to -1, and trace average of 2s orbitals to 15") OperatorSetTrace(O,-1,Indices["1s"]) OperatorSetTrace(O,15,Indices["2s"]) print(O)
Result
Operator: Operator QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 4 (largest number of product of lader operators) NFermionic modes = 4 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 4 (number of operators of length 2) C 0 A 0 | 1.000000000000000E+00 C 1 A 1 | 1.000000000000000E+00 C 2 A 2 | 2.000000000000000E+00 C 3 A 3 | 2.000000000000000E+00 Operator of Length 4 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 4) C 1 C 0 A 1 A 0 | -5.000000000000000E-01 C 3 C 2 A 3 A 2 | -5.000000000000000E-01 Set Operator trace average to 0 Operator: Operator QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 4 (largest number of product of lader operators) NFermionic modes = 4 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 4 (number of operators of length 2) C 0 A 0 | -5.000000000000000E-01 C 1 A 1 | -5.000000000000000E-01 C 2 A 2 | 5.000000000000000E-01 C 3 A 3 | 5.000000000000000E-01 Operator of Length 4 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 4) C 1 C 0 A 1 A 0 | -5.000000000000000E-01 C 3 C 2 A 3 A 2 | -5.000000000000000E-01 Set Operator trace average to 2 Operator: Operator QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 4 (largest number of product of lader operators) NFermionic modes = 4 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 4 (number of operators of length 2) C 0 A 0 | 1.500000000000000E+00 C 1 A 1 | 1.500000000000000E+00 C 2 A 2 | 2.500000000000000E+00 C 3 A 3 | 2.500000000000000E+00 Operator of Length 4 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 4) C 1 C 0 A 1 A 0 | -5.000000000000000E-01 C 3 C 2 A 3 A 2 | -5.000000000000000E-01 Set trace average of 1s orbitals to -1, and trace average of 2s orbitals to 15 Operator: Operator QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 4 (largest number of product of lader operators) NFermionic modes = 4 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 4 (number of operators of length 2) C 0 A 0 | -1.000000000000000E+00 C 1 A 1 | -1.000000000000000E+00 C 2 A 2 | 1.500000000000000E+01 C 3 A 3 | 1.500000000000000E+01 Operator of Length 4 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 4) C 1 C 0 A 1 A 0 | -5.000000000000000E-01 C 3 C 2 A 3 A 2 | -5.000000000000000E-01
