2014/05/26 by Chao‐Ming Jian, Chao-Ming Jian, Xiao-Liang Qi · 78 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Mathematics #Physics #Quantum many-body systems #Statistics #String (physics) #Theoretical physics #Topological Materials and Phenomena #Topological and Geometric Data Analysis #Topology (electrical circuits) #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevx.4.041043
published in Physical Review X 4(4) (American Physical Society) · 23 pages, 17 figures
arxiv created 2014/05/26 · openalex publication_date 2014/12/10 · arxiv updated 2014/12/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
While the topological order in two dimensions has been studied extensively since the discovery of the integer and fractional quantum Hall systems, topological states in three spatial dimensions are much less understood. In this paper, we propose a general formalism for constructing a large class of threedimensional topological states by stacking layers of 2D topological states and introducing coupling between them. Using this construction, different types of topological states can be obtained, including those with only surface topological order and no bulk topological quasiparticles, and those with topological order both in the bulk and at the surface. For both classes of states, we study its generic properties and present several explicit examples. As an interesting consequence of this construction, we obtain example systems with nontrivial braiding statistics between string excitations. In addition to studying the string-string braiding in the example system, we propose a topological field-theory description for the layer-constructed systems, which captures not only the string-particle braiding statistics but also the string-string braiding statistics when the coupling is twisted. Last, we provide a proof of a general identity for Abelian string statistics and discuss an example system with non-Abelian strings.