From coupled wires to coupled layers: Model with three-dimensional fractional excitations

Abstract

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 $\mathfrak{g}$. The wires are coupled with each other to form a 3D network through the current-current interactions of ${\mathfrak{g}}_1$ and ${\mathfrak{g}}_2$ CFTs that are related to the $\mathfrak{g}$ CFT by a nontrivial conformal embedding $\mathfrak{g}\supset {\mathfrak{g}}_1\times {\mathfrak{g}}_2$. 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 point-like or loop-like deconfined excitations depending on the branching rule. We demonstrate our construction for a simple solvable model based on the conformal embedding $SU(2{)}_1\times SU(2{)}_1\supset U(1{)}_4\times U(1{)}_4$. 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 $Z_2$ gauge theory with a fermionic $Z_2$ charge.

6+10 pages, 3 figures. v2: References added, published version

References in corpus (14)

• Non-Abelian Anyons and Topological Quantum Computation
• Condensate induced transitions between topologically ordered phases
• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Twisted gauge theories in 3D Walker-Wang models
• Chiral Spin Liquids in Arrays of Spin Chains
• Layer construction of 3D topological states and string braiding statistics
• Quantum Spin Hall Effect in Strip of Stripes Model
• Composite Dirac liquids: parent states for symmetric surface topological order
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• A model of chiral spin liquids with Abelian and non-Abelian topological phases
• Three-Dimensional Fractional Topological Insulators in Coupled Rashba Layers

Cited by in corpus (1)

• Weak symmetry breaking and topological order in a 3D compressible quantum liquid