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Journal of Physics A Mathematical and General

When can an A-particle fermion wavefunction be written as a Slater determinant?

S. Rombouts, K. Heyde

Published May 7, 1994• 4 citations
Publisher

Abstract

A simple necessary and sufficient condition which tells when an A-particle fermion wavefunction can be written as a Slater determinant is proven.
DOI
10.1088/0305-4470/27/9/038

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We characterize and classify quantum correlations in two-fermion systems having 2K2K2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank); i.e., we decompose the state into a combination of elementary Slater determinants formed by pairs of mutually orthogonal single-particle states. Mixed states can be characterized by their Slater number which is the minimal Slater rank required to generate them. For K=2K=2K=2 we give a necessary and sufficient condition for a state to have a Slater number 1. We introduce a correlation measure for mixed states which can be evaluated analytically for K=2.K=2.K=2. For higher K,K,K, we provide a method of constructing and optimizing Slater number witnesses, i.e., operators that detect Slater numbers for some states.
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