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International Journal of Modern Physics C

FERMI SYSTEMS, HUBBARD MODEL AND A SYMBOLICC++ IMPLEMENTATION

Yorick Hardy, Willi-Hans Steeb

Published Feb 1, 2001• 2 citations
Publisher

Abstract

We show how the anticommutation relations for Fermi operators can be implemented with computer algebra using SymbolicC++. We describe applications to the Hubbard model. An important identity for Fermi operators is proved. Then, we test for higher order constants of motion for the Hubbard model. Finally, the matrix representation for the four point Hubbard model is calculated.

DOI
10.1142/s0129183101001638

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An algebraic model for studying quantum Fermi systems has been formulated. An embedding of the algebra of canonical anticommutation relations ( CARCARCAR ) into the Cuntz algebra O2\mathcal{O}_{2}O2​ was used. Representing this embedding on an infinite-dimensional Hilbert space forms a Fock space, on which creation and annihilation operators act, expressed in terms of the generators of the Cuntz algebra. This approach, in some cases, simplifies the calculation of various physical quantities within the second quantization method. As an example, the calculation of a two-mode partial density matrix of a bipartite fermionic system within the proposed model is presented.