The FermiFab Toolbox for Fermionic Many-Particle Quantum Systems

TL;DR

FermiFab is a computational toolbox that simplifies the manipulation and calculation of fermionic wavefunctions and reduced density matrices, making complex quantum many-particle problems more accessible for researchers.

Contribution

It introduces a symbolic computation toolbox for fermionic systems that handles antisymmetrization and creation/annihilation formalism within Matlab and Mathematica, facilitating easier quantum calculations.

Findings

Simplifies fermionic wavefunction calculations

Provides a symbolic tool for reduced density matrices

Enables hypothesis testing in 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.