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arXiv · 1301.3421

Universal Subspaces for Local Unitary Groups of Fermionic Systems

Lin Chen·Jianxin Chen·Dragomir Z. Djokovic·Bei Zeng
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Abstract

Let $\mathcal{V}=\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\ket{v_1},...,\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \ket{v_{i_1}\we v_{i_2}\we...\we v_{i_N}}$ with $i_1<... 3. If $M$ is even, the well known BCS states are not LU-equivalent to any single occupancy state. Our main result is that for N=3 and $M$ even there is a universal subspace $\cW\subseteq\cS$ spanned by $M(M-1)(M-5)/6$ states $e_{i_1,...,i_N}$. Moreover the number $M(M-1)(M-5)/6$ is minimal.

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Lin Chen, Jianxin Chen, Dragomir Z. Djokovic, Bei Zeng. 2013-03-02. Universal Subspaces for Local Unitary Groups of Fermionic Systems. https://doi.org/10.1007/s00220-014-2187-6

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