2018/09/30 by Jianlong Fu
Physics and Astronomy · #Advanced Condensed Matter Physics #Fermion #Gauge theory #MAJORANA #Majorana fermion #Mathematical physics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.98.214432
published as Phys. Rev. B 98, 214432 (2018)
openalex created_date 2018/09/27 · arxiv created 2018/10/17 · openalex publication_date 2018/12/19 · arxiv updated 2018/12/26 · openalex updated_date 2026/08/06
We explore the properties of the SO(3) Majorana representation of spin. Based on its nonlocal nature, it is shown that there is an equivalence between the SO(3) Majorana representation and the Jordan-Wigner transformation in one and two dimensions. From the relation between the SO(3) Majorana representation and one-dimensional Jordan-Wigner transformation, we show that application of the SO(3) Majorana representation usually results in Z2 gauge structure. Based on lattice Chern-Simons gauge theory, it is shown that the anticommuting link variables in the SO(3) Majorana representation make it equivalent to an operator form of compact U(1)1 Chern-Simons Jordan-Wigner transformation in 2D. As examples of its application, we discuss two spin models, namely the quantum XY model on a honeycomb lattice and the 90^\ensuremath∘ compass model on a square lattice. It is shown that under the SO(3) Majorana representation both spin models can be exactly mapped into Z2 gauge theory of spinons, with the standard form of Z2 Gauss law constraint.