{"paper":{"title":"Universal Subspaces for Local Unitary Groups of Fermionic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bei Zeng, Dragomir Z. Djokovic, Jianxin Chen, Lin Chen","submitted_at":"2013-01-15T17:17:10Z","abstract_excerpt":"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 $i_1<...<i_N$ form an o.n. basis of $\\cV$. Let $\\cS\\subseteq\\cV$ be the subspace spanned by all $e_{i_1,...,i_N}$ such that the set $\\{i_1,...,i_N\\}$ contains no pair $\\{2k-1,2k\\}$, $k$ an integer. We say that the $\\ket{\\psi}\\in\\cS$ are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3421","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}