2019/01/31 by Yohei Fuji, Akira Furusaki · 1 citation
Mathematics · Physics and Astronomy · #Anyon #Central charge #Conformal field theory #Conformal map #Degenerate energy levels #Embedding #Geometry #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Quasiparticle #Superconductivity #Topological Materials and Phenomena #Topological quantum computer #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.99.241107
published as Phys. Rev. B 99, 241107 (2019) · 6+10 pages, 3 figures. v2: References added, published version
openalex publication_date 2019/06/12 · arxiv created 2019/06/13 · arxiv updated 2019/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional conformal field theory (CFT) associated with a current algebra \mathfrakg. The wires are coupled with each other to form a 3D network through the current-current interactions of \mathfrakg1 and \mathfrakg2 CFTs that are related to the \mathfrakg CFT by a nontrivial conformal embedding \mathfrakg\ensuremath⊃\mathfrakg1\ifmmode×\else\texttimes\fi\mathfrakg2. The resulting model can be viewed as a layer construction of a 3D topologically ordered state, in which the conformal embedding in each wire implements the anyon condensation between adjacent layers. Local operators acting on the ground state create pointlike or looplike deconfined excitations depending on the branching rule. We demonstrate our construction for a simple solvable model based on the conformal embedding SU(2)1\ifmmode×\else\texttimes\fiSU(2)1\ensuremath⊃U(1)4\ifmmode×\else\texttimes\fiU(1)4. We show that the model possesses extensively degenerate ground states on a torus with deconfined quasiparticles, and that appropriate local perturbations lift the degeneracy and yield a 3D Z2 gauge theory with a fermionic Z2 charge.