NewOperator

NewOperator(name, …) creates one of the standard operators as described in the section on standard operators.

NewOperator(Nf, Nb, CreationTable) can be used to create any operator of the form: $$\begin{eqnarray} \nonumber O = && \alpha^{(0,0)} 1 \\ \nonumber + \sum_i && \alpha^{(1,0)}_i a^{\dagger}_i + \alpha^{(0,1)}_i a_i \\ \nonumber + \sum_{i,j} && \alpha^{(2,0)}_{i,j} a^{\dagger}_ia^{\dagger}_j + \alpha^{(1,1)}_{i,j} a^{\dagger}_ia_j + \alpha^{(0,2)}_{i,j} a_ia_j \\ + \sum_{i,j,k} && ... . \end{eqnarray}$$ The format of CreationTable for the above listed operator is: NewOperator(Nf, Nb, { {$i_1$,$j_1$,$k_1$,$\alpha_{i,j,k}$},{$i_1$,$j_1$,$\alpha_{i,j}$},…}) Whereby positive indices create a particle, negative indices annihilate a particle. Index $i$ for 0 to Nf-1 label Fermions, from Nf to Nf+Nb label Bosons. $\alpha$ can be either a real or a complex number. NewOperator can take a forth element specifying options.

• Nf : Integer
• Nb : Integer
• CreationTable : Table of tables, whereby each table is a list of orbital indices where a particle needs to be created (positive) or annihilated (negative) and a prefactor (real or complex number). Note that -0 and +0 are different.
• Possible options

  • “Restrictions” A list specifying restrictions when applying the operator to a wave-function.
  • “Name” a string specifying the name of the operator
  • “NBitsKey” a list of integers specifying the number of bits in the key used for the hash lookup tables. Only useful when a lot of operations are done on the operators. Not used when Operator * Wavefunction is calculated.

• O : Operator

description text

NewOperator.Quanty

Nf = 5
Nb = 0
O = NewOperator(Nf, Nb, {{             10},
                         {0,-0,         3},
                         {0,1,2,3,4,  1+I}},
                {{"Name","Liberty"}})
print(O)

NewOperator.out

Operator: Liberty
QComplex         =          2 (Real==0 or Complex==1 or Mixed==2)
MaxLength        =          5 (largest number of product of lader operators)
NFermionic modes =          5 (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+01
 
Operator of Length   2
QComplex      =          0 (Real==0 or Complex==1)
N             =          1 (number of operators of length   2)
C  0 A  0 |  3.00000000000000E+00
 
Operator of Length   5
QComplex      =          1 (Real==0 or Complex==1)
N             =          1 (number of operators of length   5)
C  4 C  3 C  2 C  1 C  0 |  1.00000000000000E+00  1.00000000000000E+00