Partition Functions of Strongly Correlated Electron Systems as "Fermionants"

Details Partition Functions of Strongly Correlated Electron Systems as "Fermionants" Partition Functions of Strongly Correlated Electron Systems as "Fermionants"

2011-08-11

arxiv.org/abs/1108.2461v1

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, no figures

Scientific paper

We introduce a new mathematical object, the "fermionant" ${\mathrm{Ferm}}_N(G)$, of type $N$ of an $n \times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces to the determinant. The partition function of the repulsive Hubbard model, of geometrically frustrated quantum antiferromagnets, and of Kondo lattice models can be expressed as fermionants of type N=2, which naturally incorporates infinite on-site repulsion. A computation of the fermionant in polynomial time would solve many interesting fermion sign problems.

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