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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.
Input
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Nf : Integer
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Nb : Integer
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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.
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Possible options
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“Restrictions” A list specifying restrictions when applying the operator to a wave-function.
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“Name” a string specifying the name of the operator
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“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.
Output
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O : Operator
Example
description text
Input
- 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)
Result
- 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) | 1.000000000000000E+01 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 | 1.000000000000000E+00 1.000000000000000E+00
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