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documentation:language_reference:functions:operatorsettrace [2018/09/26 14:40] – Added Code Example and corrected some statements Simon Heinzedocumentation:language_reference:functions:operatorsettrace [2025/11/20 03:29] (current) – external edit 127.0.0.1
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 ====== OperatorSetTrace ====== ====== OperatorSetTrace ======
  
-### +Deprecated, with next release use //[[documentation:language_reference:functions:OperatorSetOnsiteEnergy|OperatorSetOnsiteEnergy()]]//, which has the same behaviour.
-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 +
-  * $t$ : New value of the trace average (Default 0) +
-  * {$i_1,...,i_n$} : List of indices (Default {$0,...,N_{Fermi}-1$}) +
- +
-===== Output ===== +
- +
-  * $O^\prime$ : Operator with newly set trace +
- +
-===== Example ===== +
- +
- +
-==== Input ==== +
-<code Quanty 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) +
-</code> +
- +
-==== Result ==== +
-<file Quanty_Output> +
-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 +
- +
-</file>+
  
 ===== Table of contents ===== ===== Table of contents =====
 {{indexmenu>.#1}} {{indexmenu>.#1}}
  

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