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.

arXiv comment6+10 pages, 3 figures. v2: References added, published version

References in corpus (56)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• String-net condensation: A physical mechanism for topological phases
• Bosonization and Strongly Correlated Systems
• Symmetry Protected Topological phases of Quantum Matter
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Condensate induced transitions between topologically ordered phases
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
• The Fractional Quantum Hall effect in an array of quantum wires
• Boson topological insulators: A window into highly entangled quantum phases
• From Luttinger liquid to non-Abelian quantum Hall states
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Three-dimensional topological lattice models with surface anyons
• A theory of 2+1D bosonic topological orders
• Wire deconstructionism of two-dimensional topological phases
• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
• Hamiltonian models for topological phases of matter in three spatial dimensions
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Superconducting analogue of the parafermion fractional quantum Hall states
• Twisted gauge theories in 3D Walker-Wang models
• Non-Abelian topological insulators from an array of quantum wires
• 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
• A classification of 3+1D bosonic topological orders (II): the case when some point-like excitations are fermions
• Pairing in Luttinger Liquids and Quantum Hall States
• Composite Dirac liquids: parent states for symmetric surface topological order
• A classification of 2D fermionic and bosonic topological orders
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Braiding with Borromean Rings in (3+1)-Dimensional Spacetime
• Wire constructions of Abelian topological phases in three or more dimensions
• Fractional topological phases in three-dimensional coupled-wire systems
• From an array of quantum wires to three-dimensional fractional topological insulators
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Loop braiding statistics in exactly soluble 3D lattice models
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Simple-current algebra constructions of 2+1D topological orders
• A model of chiral spin liquids with Abelian and non-Abelian topological phases
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Formalism for the solution of quadratic Hamiltonians with large cosine terms
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• Three-Dimensional Fractional Topological Insulators in Coupled Rashba Layers
• Worldsheet matter for electric flux strings
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Exactly soluble model of boundary degeneracy
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• A coupled wire description of surface $ADE$ topological orders

Cited by in corpus (12)

• One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
• Topological Defect Networks for Fractons of all Types
• Anisotropic layer construction of anisotropic fracton models
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Non-diagonal anisotropic quantum Hall states
• Fractonic topological phases from coupled wires
• Topological order in interacting semimetals
• Twisted coupled wire model for a moiré sliding Luttinger liquid
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Dihedral twist liquid models from emergent Majorana fermions
• Weak symmetry breaking and topological order in a 3D compressible quantum liquid