The FermiFab toolbox for fermionic many-particle quantum systems

Abstract

This paper introduces the FermiFab toolbox for many-particle quantum systems. It is mainly concerned with the representation of (symbolic) fermionic wavefunctions and the calculation of corresponding reduced density matrices (RDMs). The toolbox transparently handles the inherent antisymmetrization of wavefunctions and incorporates the creation/annihilation formalism. Thus, it aims at providing a solid base for a broad audience to use fermionic wavefunctions with the same ease as matrices in Matlab, say. Leveraging symbolic computation, the toolbox can greatly simply tedious pen-and-paper calculations for concrete quantum mechanical systems, and serves as “sandbox” for theoretical hypothesis testing. FermiFab (including full source code) is freely available as a plugin for both Matlab and Mathematica. Program summary Program title: FermiFab Catalogue identifier: AEIN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIN_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Special license provided by the author No. of lines in distributed program, including test data, etc.: 1 165 461 No. of bytes in distributed program, including test data, etc.: 15 557 308 Distribution format: tar.gz Programming language: MATLAB 7.9, Mathematica 7.0, C Computer: PCs, Sun Solaris workstation Operating system: Any platform supporting MATLAB or Mathematica; tested with Windows (32 and 64 bit) and Sun Solaris. RAM: Case dependent Classification: 4.15 Nature of problem: Representation of fermionic wavefunctions, computation of RDMs (reduced density matrices) and handing of the creation/annihilation operator formalism. Solution method: Mapping of Slater determinants to bitfields, implementation of the creation/annihilation and RDM formalism by bit operations. Running time: Depends on the problem size; several seconds for the provided demonstration files.