Batista C D, Ortiz G
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev Lett. 2001 Feb 5;86(6):1082-5. doi: 10.1103/PhysRevLett.86.1082.
We introduce a new spin-fermion mapping, for arbitrary spin S generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for S = 1/2. The mapping, valid for regular lattices in any spatial dimension d, serves to unravel hidden symmetries. We illustrate the power of the transformation by finding exact solutions to lattice models previously unsolved by standard techniques. We also show the existence of the Haldane gap in S = 1 bilinear nearest-neighbor Heisenberg spin chains and discuss the relevance of the mapping to models of strongly correlated electrons. Moreover, we present a general spin-anyon mapping for the case d < or = 2.
我们引入了一种新的自旋-费米子映射，用于生成SU(2)群代数的任意自旋S，它是S = 1/2时约旦-维格纳变换的自然推广。该映射适用于任意空间维度d的规则晶格，有助于揭示隐藏的对称性。我们通过找到标准技术之前未解决的晶格模型的精确解来说明这种变换的强大之处。我们还展示了S = 1双线性最近邻海森堡自旋链中霍尔丹能隙的存在，并讨论了该映射与强关联电子模型的相关性。此外，我们给出了d≤2情况下的一般自旋任意子映射。
