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documentation:tutorials:introduction_to_quanty:operators_2 [2016/10/07 20:21] – created Maurits W. Haverkortdocumentation:tutorials:introduction_to_quanty:operators_2 [2025/11/20 03:29] (current) – external edit 127.0.0.1
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 +{{indexmenu_n>3}}
 +====== Operators continued ======
  
 +###
 +The third examples shows several standard operators acting on a $p$-shell.
 +###
 +
 +###
 +<code Quanty Operators_continued.Quanty>
 +-- A basis consists of:
 + -- a number of Fermionic modes or spin-orbitals
 +NF=6;
 + -- a number of Bosonic modes (phonon modes, ...)
 +NB=0;
 + -- an index relating the spinorbitals to quantum 
 + -- numbers we assign to them.  For a p-shell we would
 + -- like the have 6 spinorbitals with the quantum
 + -- numbers spin up ml=-1,ml=0,ml=1 and spin down
 + -- with ml=-1, ml=0, ml=1
 +IndexDn={0,2,4};
 +IndexUp={1,3,5};
 +-- the code knows that a 3 fold degenerate shell 
 +-- has l=1 and ml=-1, 0 and 1 are assigned to 
 +-- them automatically
 +
 +-- we can now create the spin operators on this basis
 +OppSx=NewOperator("Sx",NF,IndexUp,IndexDn);
 +OppSy=NewOperator("Sy",NF,IndexUp,IndexDn);
 +OppSz=NewOperator("Sz",NF,IndexUp,IndexDn);
 +
 +-- and print them
 +print(OppSx)
 +print(OppSy)
 +print(OppSz)
 +
 +print("=================================");
 +-- the spin operators commute such that 
 +-- Sx * Sy - Sy * Sx = I Sz. This can easily be 
 +-- checked by multiplying operators
 +OppNill = OppSx * OppSy - OppSy * OppSx - I * OppSz;
 +
 +-- OppNill should be a zero operator
 +print(OppNill)
 +
 +-- Printing indeed showed only zero's, but the are 
 +-- still stored. The above equation should return
 +-- an operator of lenght zero. in order to remove
 +-- small values from the operator one can chop these
 +OppNill=Chop(OppNill);
 +
 +-- secondly the name of the operator is a generic 
 +-- "operator". Not so nice, so lets set the name
 +OppNill.Name = "Sx * Sy - Sy * Sx - I Sz";
 +
 +-- now we can print again.
 +print(OppNill)
 +</code>
 +###
 +
 +###
 +The output is:
 +<file Quanty_Output Operators_continued.out>
 +Operator: Sx
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          2 (largest number of product of lader operators)
 +NFermionic modes =          6 (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             =          6 (number of operators of length   2)
 +C  0 A  1 |  5.000000000000000E-01
 +C  1 A  0 |  5.000000000000000E-01
 +C  2 A  3 |  5.000000000000000E-01
 +C  3 A  2 |  5.000000000000000E-01
 +C  4 A  5 |  5.000000000000000E-01
 +C  5 A  4 |  5.000000000000000E-01
 +
 +
 +
 +Operator: Sy
 +QComplex         =          1 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          2 (largest number of product of lader operators)
 +NFermionic modes =          6 (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      =          1 (Real==0 or Complex==1)
 +N             =          6 (number of operators of length   2)
 +C  0 A  1 |  0.000000000000000E+00  5.000000000000000E-01
 +C  1 A  0 |  0.000000000000000E+00 -5.000000000000000E-01
 +C  2 A  3 |  0.000000000000000E+00  5.000000000000000E-01
 +C  3 A  2 |  0.000000000000000E+00 -5.000000000000000E-01
 +C  4 A  5 |  0.000000000000000E+00  5.000000000000000E-01
 +C  5 A  4 |  0.000000000000000E+00 -5.000000000000000E-01
 +
 +
 +
 +Operator: Sz
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          2 (largest number of product of lader operators)
 +NFermionic modes =          6 (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             =          6 (number of operators of length   2)
 +C  1 A  1 |  5.000000000000000E-01
 +C  0 A  0 | -5.000000000000000E-01
 +C  3 A  3 |  5.000000000000000E-01
 +C  2 A  2 | -5.000000000000000E-01
 +C  5 A  5 |  5.000000000000000E-01
 +C  4 A  4 | -5.000000000000000E-01
 +
 +
 +=================================
 +
 +Operator: Operator
 +QComplex         =          1 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (largest number of product of lader operators)
 +NFermionic modes =          6 (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      =          1 (Real==0 or Complex==1)
 +N             =          6 (number of operators of length   2)
 +C  1 A  1 |  0.000000000000000E+00  0.000000000000000E+00
 +C  0 A  0 |  0.000000000000000E+00  0.000000000000000E+00
 +C  3 A  3 |  0.000000000000000E+00  0.000000000000000E+00
 +C  2 A  2 |  0.000000000000000E+00  0.000000000000000E+00
 +C  5 A  5 |  0.000000000000000E+00  0.000000000000000E+00
 +C  4 A  4 |  0.000000000000000E+00  0.000000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          1 (Real==0 or Complex==1)
 +N             =         15 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.000000000000000E+00  0.000000000000000E+00
 +C  2 C  0 A  3 A  1 |  0.000000000000000E+00  0.000000000000000E+00
 +C  3 C  0 A  2 A  1 |  0.000000000000000E+00  0.000000000000000E+00
 +C  4 C  0 A  5 A  1 |  0.000000000000000E+00  0.000000000000000E+00
 +C  5 C  0 A  4 A  1 |  0.000000000000000E+00  0.000000000000000E+00
 +C  2 C  1 A  3 A  0 |  0.000000000000000E+00  0.000000000000000E+00
 +C  3 C  1 A  2 A  0 |  0.000000000000000E+00  0.000000000000000E+00
 +C  4 C  1 A  5 A  0 |  0.000000000000000E+00  0.000000000000000E+00
 +C  5 C  1 A  4 A  0 |  0.000000000000000E+00  0.000000000000000E+00
 +C  3 C  2 A  3 A  2 |  0.000000000000000E+00  0.000000000000000E+00
 +C  4 C  2 A  5 A  3 |  0.000000000000000E+00  0.000000000000000E+00
 +C  5 C  2 A  4 A  3 |  0.000000000000000E+00  0.000000000000000E+00
 +C  4 C  3 A  5 A  2 |  0.000000000000000E+00  0.000000000000000E+00
 +C  5 C  3 A  4 A  2 |  0.000000000000000E+00  0.000000000000000E+00
 +C  5 C  4 A  5 A  4 |  0.000000000000000E+00  0.000000000000000E+00
 +
 +
 +
 +Operator: Sx * Sy - Sy * Sx - I Sz
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (largest number of product of lader operators)
 +NFermionic modes =          6 (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)
 +</file>
 +###
 +
 +
 +===== Table of contents =====
 +{{indexmenu>.#1|msort}}

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