@article {1450,
title = {Universal Subspaces for Local Unitary Groups of Fermionic Systems},
journal = {Communications in Mathematical Physics},
volume = {333},
year = {2015},
month = {2014/10/10},
pages = {541 - 563},
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.
},
doi = {10.1007/s00220-014-2187-6},
url = {http://arxiv.org/abs/1301.3421v2},
author = {Lin Chen and Jianxin Chen and Dragomir Z. Djokovic and Bei Zeng}
}