



01286nas a2200157   4500008004100000245005300041210005300094260001500147300001100162490000700173520086500180100001801045700001401063700001401077856003701091       2014                        eng d00aUnextendible Product Basis for Fermionic Systems0 aUnextendible Product Basis for Fermionic Systems  c2014/01/01  a0822070 v553 a  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.
1 aChen, Jianxin1 aChen, Lin1 aZeng, Bei  uhttp://arxiv.org/abs/1312.4218v1