@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}
}
@article {1445,
title = {Unextendible Product Basis for Fermionic Systems},
journal = {Journal of Mathematical Physics},
volume = {55},
year = {2014},
month = {2014/01/01},
pages = {082207},
abstract = { We discuss the concept of unextendible product basis (UPB) and generalized
UPB for fermionic systems, using Slater determinants as an analogue of product
states, in the antisymmetric subspace $\wedge^ N \bC^M$. We construct an
explicit example of generalized fermionic unextendible product basis (FUPB) of
minimum cardinality $N(M-N)+1$ for any $N\ge2,M\ge4$. We also show that any
bipartite antisymmetric space $\wedge^ 2 \bC^M$ of codimension two is spanned
by Slater determinants, and the spaces of higher codimension may not be spanned
by Slater determinants. Furthermore, we construct an example of complex FUPB of
$N=2,M=4$ with minimum cardinality $5$. In contrast, we show that a real FUPB
does not exist for $N=2,M=4$ . Finally we provide a systematic construction for
FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.
},
doi = {10.1063/1.4893358},
url = {http://arxiv.org/abs/1312.4218v1},
author = {Jianxin Chen and Lin Chen and Bei Zeng}
}