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SNEG - Package for calculations using the operators of second quantization

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  • Subject: [mg71255] SNEG - Package for calculations using the operators of second quantization
  • From: Rok Zitko <rokzitko at>
  • Date: Sun, 12 Nov 2006 06:47:37 -0500 (EST)
  • Organization: Institute Jozef Stefan

I have written a Mathematica package "SNEG" for performing calculations
using the operators of the second quantization formalism of quantum
mechanics (with an emphasis on the anti-commuting fermionic operators). I
have used the package extensively in the past years to solve various
problems in theoretical condensed-matter and many-particle physics, so it
has been well tested. Working with the package is especially nice when used
in conjunction with the Notation package to obtain answers in the form that
most physicists are familiar with. The package is freely (GPL license)
available from

Apart from defining a non-commutative multiplication with automatic
reordering of operators in the conventional normal ordered products, the
package has a number of additional features, such as:
- utility functions to generate various operator expressions (electron
  number, spin operators, hopping operators,...);
- manipulations of operator expressions: canonic conjugation, spin 
- calculations of vacuum expectation values;
- occupation-number representations of states;
- Dirac's bra-ket notation;
- support for summation over dummy indexes and simplification of such
- generation of basis states on lattices with well defined particle
  number and spin, well defined isospin (axial charge) and spin, etc.;
- simplifications using the Wick's theorem.

Perhaps the nicest thing about the package is that it takes away the dreaded
minus-sign errors when commuting the fermionic operators in complex operator
expressions. In the past, "SNEG" has been applied to perform exact
diagonalizations on Hubbard clusters, calculations of commutators of complex
expressions, perturbation theory to higher orders, numerical renormalization
group (NRG) calculations, etc.  I hope the package will be useful to the

Rok Zitko, rok.zitko at
Jozef Stefan Institute
Ljubljana, Slovenia

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