SNEG - Package for calculations using the operators of second quantization

*To*: mathgroup at smc.vnet.net*Subject*: [mg71255] SNEG - Package for calculations using the operators of second quantization*From*: Rok Zitko <rokzitko at gmail.com>*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 http://auger.ijs.si/ljubljana/sneg 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 inversion; - 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 expressions; - 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 community. Rok Zitko, rok.zitko at ijs.si Jozef Stefan Institute Ljubljana, Slovenia