2021/01/09 by Ning Wang, Wang, Ning, Qiao Zhuang +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum many-body systems #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2101.03359
openalex publication_date 2021/01/09 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28
Symmetry-protected topological (SPT) phases are gapped short-range entangled states with symmetry G, which can be systematically described by group cohomology theory. SU(3) and SU(2)×U(1) are considered as the basic groups of Quantum Chromodynamics and Weak-Electromagnetic unification, respectively. In two dimension (2D), nonlinear-sigma models with a quantized topological Theta term can be used to describe nontrivial SPT phases. By coupling the system to a probe field and integrating out the group variables, the Theta term becomes the effective action of Chern-Simons theory which can derive the response current density. As a result, the current shows a spin Hall effect, and the quantized number of the spin Hall conductance of SPT phases SU(3) and SU(2)×U(1) are same. In addition, relationships between SU(3) and SU(2)×U(1) which maps SU(3) to SU(2) with a rotation U(1) will be given.