Operators continued
The third examples shows several standard operators acting on a $p$-shell.
- 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)
The output is:
- 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)
