- 范畴和拓扑序讨论班

Gapless and symmetry breaking phases in one-dimensional generalized Kitaev spin-1/2 models with nonsymmorphic symmetries

组织者

郑浩

演讲者

杨望

时间

2022年04月13日 13:30 至 15:00

地点

1131

线上

Tencent 660 7557 3050 ()

摘要

Kitaev materials on the honeycomb lattice have attracted intense research interests in the past decade because of their potential in realizing topological quantum computations. Motivated by the analytical and numerical difficulties in strongly correlated two-dimensional (2D) systems, we have performed a series of studies on 1D generalized Kitaev spin models, hoping that they can provide hints for 2D Kitaev physics. In addition, these 1D models are also intriguing on their own, since they contain rich nonsymmorphic group structures. In this talk, I will first discuss our work on the 1D spin-1/2 Kitaev-Gamma model. The model is proved to have a hidden nonsymmophic symmetry group, which is isomorphic to a nontrivial group extension of the O_h group by Z, where O_h is the full octahedral group. Using field theory and symmetry analysis, we are able to analytically demonstrate the existence of an extended gapless phase with an emergent SU(2)_1 conformal symmetry at low energies, which is confirmed by our density matrix renormalization group numerical simulations. Besides the gapless phase, there are two magnetically ordered phases with symmetry breaking patterns O_h→D_4 and O_h→D_3, where D_n is the dihedral group of order 2n. After this, I will briefly talk about the more general 1D spin-1/2 Kitaev-Heisenberg-Gamma model. I will focus on two Luttinger liquid phases in the phase diagram, and show that the 2D zigzag magnetic order can be obtained from one of the two Luttinger liquid phases by weakly coupling an infinite number of 1D chains.