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documentation:language_reference:functions:partialoperator [2018/08/03 14:48] – created Simon Heinzedocumentation:language_reference:functions:partialoperator [2022/10/04 22:08] (current) Maurits W. Haverkort
Line 1: Line 1:
 ====== PartialOperator ====== ====== PartialOperator ======
  
-(will be published in fall 2018)+### 
 +PartialOperator(//op//,//indices//,//mode//takes an operator and a list of indices and depending on //mode// removes or keeps specific terms. 
 +### 
 + 
 +### 
 +Mode //"include"// keeps all terms whereby at least one of the creation or annihilation operators acts on the orbitals included in the list //indices//
 +### 
 + 
 +### 
 +Mode //"exclude"// removes all terms whereby at least one of the creation or annihilation operators acts on the orbitals included in the list //indices//
 +###
  
 ### ###
-PartialOperator(//op//,//indices//) takes an operator and a list of indices and returns any part of //op// that acts on the index-set //indices//.+Mode //"conserve"// removes all terms that do not keep the occupation conserved from the orbitals listed in the table //indices//. In this case the table //indices// is allowed to include tablesIn the latter case the sum of the occupation all orbitals in the list needs to be conserved
 ### ###
  
Line 11: Line 21:
   * //op// : An Operator.   * //op// : An Operator.
   * //indices// : A list of indices.   * //indices// : A list of indices.
 +  * //mode// : either "include", "exclude", or "conserve"
  
 ===== Output ===== ===== Output =====
  
-  * //partialOp// : The part of //op// acting on //indices//.+  * //partialOp// : The operator with a subset of terms of the original operator.
  
 ===== Example ===== ===== Example =====
Line 20: Line 31:
 ==== Input ==== ==== Input ====
 <code Quanty Example.Quanty> <code Quanty Example.Quanty>
-NF = 4+NF = 
 +NB = 0
  
 +opp1cr = NewOperator(NF,NB, {{ 0,1},{ 1,1},{ 2,1}})
 +opp1an = NewOperator(NF,NB, {{-0,1},{-1,1},{-2,1}})
 +opp2 = opp1cr * opp1an
 +opp3 = opp1an * opp2
 +opp4 = opp1cr * opp3
  
-op1 NewOperator("Number",NF,{1},{1},{0.1+I}) NewOperator("U",NF,{0},{1},{5}) +opp = 1 + opp1cr opp1an opp2 opp3 opp4
-op2 = NewOperator("Number",NF,{1},{1},{0.00001 I}) NewOperator("Number",NF,{2},{2},{1}) + NewOperator("U",NF,{0},{1},{0},{1},{2},{3},{2},{3},{3}) + NewOperator("U",NF,{0},{1},{5})+
  
-print("op1:") +-- The operatore contains strings of creation and annihilation operators of length 0 to 4 
-print(op1+-- l=0  1 term 
-print("PartialOperator(op1, {0,1})") +-- l=1  6 terms (3 creation, 3 annihilation) 
-print(PartialOperator(op1, {0,1})) +-- l=2  9 terms (3 creation * 3 annihilation) 
-print("PartialOperator(op1, {2})") +-- l=3  9 terms (cr an an) note that an0 an1 = - an1 an0 
-print(PartialOperator(op1, {2})) +-- l=4  9 terms  
-print("\n\n\n") +-- the full operator is 
-print("op2:") +print("================ opp =============") 
-print(op2+print(opp) 
-print("PartialOperator(op2, {0,1})") + 
-print(PartialOperator(op2, {0,1})) +-- We only keep terms that at least act once on orbital 1 
-print("PartialOperator(op2, {2})"+print("================ PartialOperator  {1} include =============") 
-print(PartialOperator(op2, {2}))+print(PartialOperator(opp,{1},"include")) 
 + 
 +-- We only keep terms that at least act once on orbital 0 or at orbital 1 
 +print("================ PartialOperator  {0,2} include =============") 
 +print(PartialOperator(opp,{0,2},"include")) 
 + 
 +-- We remove all terms that act on orbital 1 
 +print("================ PartialOperator  {1} exclude =============") 
 +print(PartialOperator(opp,{1},"exclude")) 
 + 
 +-- We exclude all terms that act on orbital 0 and we exclude all terms that act on orbital 2 
 +print("================ PartialOperator  {0,2} exclude ============="
 +print(PartialOperator(opp,{0,2},"exclude")
 + 
 +-- We only keep the terms that keep the occupation of orbital 1 conserved 
 +print("================ PartialOperator  {1} conserve =============") 
 +print(PartialOperator(opp,{1},"conserve")) 
 + 
 +-- We only keep the terms that keep the occupation of orbital 0 conserved and that keep 
 +-- the occupation of orbital 2 conserved 
 +print("================ PartialOperator  {0,2} conserve ============="
 +print(PartialOperator(opp,{0,2},"conserve")
 + 
 +-- We only keep those terms that keep the sum of the occupation of orbital 0 and 2 conserved 
 +print("================ PartialOperator  {{0,2}} conserve =============") 
 +print(PartialOperator(opp,{{0,2}},"conserve"))
 </code> </code>
  
 ==== Result ==== ==== Result ====
 <file Quanty_Output> <file Quanty_Output>
-op1:+================ opp =============
  
-Operator: CrAn +Operator: Operator 
-QComplex                  (Real==0 or Complex==1 or Mixed==2)+QComplex                  (Real==0 or Complex==1 or Mixed==2)
 MaxLength        =          4 (largest number of product of lader operators) MaxLength        =          4 (largest number of product of lader operators)
-NFermionic modes =          (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)+NFermionic modes =          (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) NBosonic modes            0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
  
Line 54: Line 95:
 QComplex      =          0 (Real==0 or Complex==1) QComplex      =          0 (Real==0 or Complex==1)
 N                      1 (number of operators of length   0) N                      1 (number of operators of length   0)
-|  3.000000000000000E+00+|  1.00000000000000E+00 
 + 
 +Operator of Length   1 
 +QComplex      =          0 (Real==0 or Complex==1) 
 +N                      6 (number of operators of length   1) 
 +C  0 |  1.00000000000000E+00 
 +C  1 |  1.00000000000000E+00 
 +C  2 |  1.00000000000000E+00 
 +A  0 |  4.00000000000000E+00 
 +A  1 |  4.00000000000000E+00 
 +A  2 |  4.00000000000000E+00
  
 Operator of Length   2 Operator of Length   2
-QComplex      =          (Real==0 or Complex==1) +QComplex      =          (Real==0 or Complex==1) 
-N                      (number of operators of length   2) +N                      (number of operators of length   2) 
-C  1 A  1 |  1.000000000000000E-01  1.000000000000000E+00+C  0 A  0 |  4.00000000000000E+00 
 +C  1 A  0 |  4.00000000000000E+00 
 +C  2 A  0 |  4.00000000000000E+00 
 +C  0 A  1 |  4.00000000000000E+00 
 + A  1 |  4.00000000000000E+00 
 +C  2 A  |  4.00000000000000E+00 
 +C  0 A  2 |  4.00000000000000E+00 
 +C  1 A  2 |  4.00000000000000E+00 
 +C  2 A  2 |  4.00000000000000E+00 
 + 
 +Operator of Length   3 
 +QComplex      =          0 (Real==0 or Complex==1) 
 +N                      9 (number of operators of length   3) 
 +C  0 A  1 A  0 |  0.00000000000000E+00 
 +C  0 A  2 A  0 |  0.00000000000000E+00 
 +C  1 A  1 A  0 |  0.00000000000000E+00 
 +C  1 A  2 A  0 |  0.00000000000000E+00 
 +C  2 A  1 A  0 |  0.00000000000000E+00 
 +C  2 A  2 A  0 |  0.00000000000000E+00 
 +C  0 A  2 A  1 |  0.00000000000000E+00 
 +C  1 A  2 A  1 |  0.00000000000000E+00 
 +C  2 A  2 A  1 |  0.00000000000000E+00
  
 Operator of Length   4 Operator of Length   4
 QComplex      =          0 (Real==0 or Complex==1) QComplex      =          0 (Real==0 or Complex==1)
-N                      (number of operators of length   4) +N                      (number of operators of length   4) 
-C  1 C  0 A  1 A  0 | -5.000000000000000E+00+C  1 C  0 A  1 A  0 |  0.00000000000000E+00 
 +C  2 C  0 A  1 A  0 |  0.00000000000000E+00 
 +C  1 C  0 A  2 A  0 |  0.00000000000000E+00 
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00 
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00 
 +C  2 C  1 A  2 A  0 |  0.00000000000000E+00 
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00 
 +C  2 C  0 A  2 A  1 |  0.00000000000000E+00 
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
  
  
-PartialOperator(op1, {0,1})+================ PartialOperator  {1} include =============
  
 Operator:  Operator: 
-QComplex                  (Real==0 or Complex==1 or Mixed==2)+QComplex                  (Real==0 or Complex==1 or Mixed==2)
 MaxLength        =          4 (largest number of product of lader operators) MaxLength        =          4 (largest number of product of lader operators)
-NFermionic modes =          (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)+NFermionic modes =          (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) NBosonic modes            0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
  
 Operator of Length   2 Operator of Length   2
-QComplex      =          (Real==0 or Complex==1) +QComplex      =          (Real==0 or Complex==1) 
-N                      (number of operators of length   2) +N                      (number of operators of length   2) 
-C  1 A  1 |  1.000000000000000E-01  1.000000000000000E+00+C  1 A  0 |  4.00000000000000E+00 
 +C  0 A  1 |  4.00000000000000E+00 
 + A  1 |  4.00000000000000E+00 
 +C  2 A  |  4.00000000000000E+00 
 +C  1 A  2 |  4.00000000000000E+00 
 + 
 +Operator of Length   3 
 +QComplex      =          0 (Real==0 or Complex==1) 
 +N                      7 (number of operators of length   3) 
 +C  0 A  1 A  0 |  0.00000000000000E+00 
 +C  1 A  1 A  0 |  0.00000000000000E+00 
 +C  1 A  2 A  0 |  0.00000000000000E+00 
 +C  2 A  1 A  0 |  0.00000000000000E+00 
 +C  0 A  2 A  1 |  0.00000000000000E+00 
 +C  1 A  2 A  1 |  0.00000000000000E+00 
 +C  2 A  2 A  1 |  0.00000000000000E+00
  
 Operator of Length   4 Operator of Length   4
 QComplex      =          0 (Real==0 or Complex==1) QComplex      =          0 (Real==0 or Complex==1)
-N                      (number of operators of length   4) +N                      (number of operators of length   4) 
-C  1 C  0 A  1 A  0 | -5.000000000000000E+00+C  1 C  0 A  1 A  0 |  0.00000000000000E+00 
 +C  2 C  0 A  1 A  0 |  0.00000000000000E+00 
 +C  1 C  0 A  2 A  0 |  0.00000000000000E+00 
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00 
 +C  2 C  1 A  2 A  0 |  0.00000000000000E+00 
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00 
 +C  2 C  0 A  2 A  1 |  0.00000000000000E+00 
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
  
  
-PartialOperator(op1, {2})+================ PartialOperator  {0,2} include =============
  
 Operator:  Operator: 
 QComplex                  0 (Real==0 or Complex==1 or Mixed==2) QComplex                  0 (Real==0 or Complex==1 or Mixed==2)
 MaxLength        =          4 (largest number of product of lader operators) MaxLength        =          4 (largest number of product of lader operators)
-NFermionic modes =          (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)+NFermionic modes =          (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) NBosonic modes            0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
  
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      4 (number of operators of length   1)
 +C  0 |  1.00000000000000E+00
 +C  2 |  1.00000000000000E+00
 +A  0 |  4.00000000000000E+00
 +A  2 |  4.00000000000000E+00
  
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      8 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  1 A  0 |  4.00000000000000E+00
 +C  2 A  0 |  4.00000000000000E+00
 +C  0 A  1 |  4.00000000000000E+00
 +C  2 A  1 |  4.00000000000000E+00
 +C  0 A  2 |  4.00000000000000E+00
 +C  1 A  2 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
  
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      9 (number of operators of length   3)
 +C  0 A  1 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  0 |  0.00000000000000E+00
 +C  1 A  1 A  0 |  0.00000000000000E+00
 +C  1 A  2 A  0 |  0.00000000000000E+00
 +C  2 A  1 A  0 |  0.00000000000000E+00
 +C  2 A  2 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  1 |  0.00000000000000E+00
 +C  1 A  2 A  1 |  0.00000000000000E+00
 +C  2 A  2 A  1 |  0.00000000000000E+00
  
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      9 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
  
  
-op2:+================ PartialOperator  {1} exclude =============
  
-Operator: CrAn +Operator:  
-QComplex                  (Real==0 or Complex==1 or Mixed==2)+QComplex                  (Real==0 or Complex==1 or Mixed==2)
 MaxLength        =          4 (largest number of product of lader operators) MaxLength        =          4 (largest number of product of lader operators)
-NFermionic modes =          (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)+NFermionic modes =          (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) NBosonic modes            0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
 +
 +Operator of Length   0
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      1 (number of operators of length   0)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      4 (number of operators of length   1)
 +C  0 |  1.00000000000000E+00
 +C  2 |  1.00000000000000E+00
 +A  0 |  4.00000000000000E+00
 +A  2 |  4.00000000000000E+00
  
 Operator of Length   2 Operator of Length   2
-QComplex      =          (Real==0 or Complex==1) +QComplex      =          (Real==0 or Complex==1) 
-N                      (number of operators of length   2) +N                      (number of operators of length   2) 
-C  A  |  1.000000000000000E-05  1.000000000000000E+00 +C  A  |  4.00000000000000E+00 
-C  2 A  2 |  1.000000000000000E+00  0.000000000000000E+00+ 2 A  0 |  4.00000000000000E+00 
 +C  0 A  2 |  4.00000000000000E+00 
 +C  2 A  2 |  4.00000000000000E+00 
 + 
 +Operator of Length   3 
 +QComplex      =          0 (Real==0 or Complex==1
 +N                      2 (number of operators of length   3) 
 +C  0 A  2 A  0 |  0.00000000000000E+00 
 +C  2 A  2 A  0 |  0.00000000000000E+00
  
 Operator of Length   4 Operator of Length   4
 QComplex      =          0 (Real==0 or Complex==1) QComplex      =          0 (Real==0 or Complex==1)
-N                      (number of operators of length   4) +N                      (number of operators of length   4) 
-C  C  0 A  A  -3.000000000000000E+00 +C  C  0 A  A  |  0.00000000000000E+00
-C  1 C  A  1 A  0 | -5.000000000000000E+00+
  
  
-PartialOperator(op2, {0,1})+================ PartialOperator  {0,2exclude =============
  
 Operator:  Operator: 
-QComplex                  (Real==0 or Complex==1 or Mixed==2)+QComplex                  (Real==0 or Complex==1 or Mixed==2)
 MaxLength        =          4 (largest number of product of lader operators) MaxLength        =          4 (largest number of product of lader operators)
-NFermionic modes =          (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)+NFermionic modes =          (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) NBosonic modes            0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
 +
 +Operator of Length   0
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      1 (number of operators of length   0)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
  
 Operator of Length   2 Operator of Length   2
-QComplex      =          (Real==0 or Complex==1)+QComplex      =          (Real==0 or Complex==1)
 N                      1 (number of operators of length   2) N                      1 (number of operators of length   2)
-C  1 A  1 |  1.000000000000000E-05  1.000000000000000E+00+C  1 A  1 |  4.00000000000000E+00 
 + 
 + 
 +================ PartialOperator  {1} conserve ============= 
 + 
 +Operator:  
 +QComplex                  0 (Real==0 or Complex==1 or Mixed==2) 
 +MaxLength        =          4 (largest number of product of lader operators) 
 +NFermionic modes =          3 (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   0 
 +QComplex      =          0 (Real==0 or Complex==1) 
 +N                      1 (number of operators of length   0) 
 + 1.00000000000000E+00 
 + 
 +Operator of Length   1 
 +QComplex      =          0 (Real==0 or Complex==1) 
 +N                      4 (number of operators of length   1) 
 +C  0 |  1.00000000000000E+00 
 +C  2 |  1.00000000000000E+00 
 +A  0 |  4.00000000000000E+00 
 +A  2 |  4.00000000000000E+00 
 + 
 +Operator of Length   2 
 +QComplex      =          0 (Real==0 or Complex==1) 
 +N                      5 (number of operators of length   2) 
 +C  0 A  0 |  4.00000000000000E+00 
 +C  2 A  0 |  4.00000000000000E+00 
 +C  1 A  1 |  4.00000000000000E+00 
 +C  0 A  2 |  4.00000000000000E+00 
 +C  2 A  2 |  4.00000000000000E+00 
 + 
 +Operator of Length   3 
 +QComplex      =          0 (Real==0 or Complex==1) 
 +N                      4 (number of operators of length   3) 
 +C  0 A  2 A  0 |  0.00000000000000E+00 
 +C  1 A  1 A  0 |  0.00000000000000E+00 
 +C  2 A  2 A  0 |  0.00000000000000E+00 
 +C  1 A  2 A  1 |  0.00000000000000E+00
  
 Operator of Length   4 Operator of Length   4
 QComplex      =          0 (Real==0 or Complex==1) QComplex      =          0 (Real==0 or Complex==1)
-N                      (number of operators of length   4) +N                      (number of operators of length   4) 
-C  1 C  0 A  A  2 | -3.000000000000000E+00 +C  1 C  0 A   0 |  0.00000000000000E+00 
-C  1 C  0 A  A  0 | -5.000000000000000E+00+ C  0 A  2 A  0  0.00000000000000E+00 
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00 
 +C  1 C  0 A   1 |  0.00000000000000E+00 
 +C  2 C  1 A  2 A  1  0.00000000000000E+00
  
  
-PartialOperator(op2, {2})+================ PartialOperator  {0,2} conserve =============
  
 Operator:  Operator: 
-QComplex                  (Real==0 or Complex==1 or Mixed==2)+QComplex                  (Real==0 or Complex==1 or Mixed==2)
 MaxLength        =          4 (largest number of product of lader operators) MaxLength        =          4 (largest number of product of lader operators)
-NFermionic modes =          (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)+NFermionic modes =          (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) NBosonic modes            0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
 +
 +Operator of Length   0
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      1 (number of operators of length   0)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
  
 Operator of Length   2 Operator of Length   2
-QComplex      =          (Real==0 or Complex==1) +QComplex      =          (Real==0 or Complex==1) 
-N                      (number of operators of length   2) +N                      (number of operators of length   2) 
-C  2 A  2 |  1.000000000000000E+00  0.000000000000000E+00+C  0 A  0 |  4.00000000000000E+00 
 +C  1 A  1 |  4.00000000000000E+00 
 +C  2 A  2 |  4.00000000000000E+00 
 + 
 +Operator of Length   3 
 +QComplex      =          0 (Real==0 or Complex==1
 +N                      2 (number of operators of length   3) 
 +C  0 A  1 A  0 |  0.00000000000000E+00 
 +C  2 A  2 A  1 |  0.00000000000000E+00
  
 Operator of Length   4 Operator of Length   4
 QComplex      =          0 (Real==0 or Complex==1) QComplex      =          0 (Real==0 or Complex==1)
-N                      (number of operators of length   4) +N                      (number of operators of length   4) 
-C  1 C  0 A  A  2 | -3.000000000000000E+00+C  1 C  0 A   0 |  0.00000000000000E+00 
 + C  0 A  2 A  0  0.00000000000000E+00 
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
  
  
 +================ PartialOperator  {{0,2}} conserve =============
  
 +Operator: 
 +QComplex                  0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (largest number of product of lader operators)
 +NFermionic modes =          3 (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   0
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      1 (number of operators of length   0)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      5 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  2 A  0 |  4.00000000000000E+00
 +C  1 A  1 |  4.00000000000000E+00
 +C  0 A  2 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      4 (number of operators of length   3)
 +C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 A  1 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 A  2 A  1 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N                      5 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
 </file> </file>
  
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