Dihedral twist liquid models from emergent Majorana fermions

Abstract

We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute the $SO(N)$ Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedral $D_k$ symmetry of $SO(2n{)}_1$, and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the $\mathcal{C}/G$ twist liquids, where $G={\mathbb{Z}}_2$ for $\mathcal{C}=U(1{)}_l$, $SU(n{)}_1$, and $G={\mathbb{Z}}_2$, ${\mathbb{Z}}_k$, $D_k$ for $\mathcal{C}=SO(2n{)}_1$. We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern in $SO(2n{)}_1/G$ by identifying the non-chiral components of the twist liquids with discrete gauge theories.

arXiv comment75 pages, 4 figures

References in corpus (124)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• String-net condensation: A physical mechanism for topological phases
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological orders and Edge excitations in FQH states
• Quantum Orders and Symmetric Spin Liquids
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Zoo of quantum-topological phases of matter
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Braiding statistics approach to symmetry-protected topological phases
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Models for gapped boundaries and domain walls
• Particle-hole symmetry and the Pfaffian state
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Quantum orders in an exact soluble model
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Is the Composite Fermion a Dirac Particle?
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• TFT construction of RCFT correlators I: Partition functions
• Condensate induced transitions between topologically ordered phases
• Topological Order and Conformal Quantum Critical Points
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Measurement-Only Topological Quantum Computation
• A classification of symmetry enriched topological phases with exactly solvable models
• Genons, twist defects, and projective non-Abelian braiding statistics
• The Fractional Quantum Hall effect in an array of quantum wires
• From Luttinger liquid to non-Abelian quantum Hall states
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Quantum Theory of the Smectic Metal State in Stripe Phases
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Anyon condensation and its applications
• Two dimensional anisotropic non Fermi-liquid phase of coupled Luttinger liquids
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Symmetry fractionalization and twist defects
• Anyon computers with smaller groups
• Wire deconstructionism of two-dimensional topological phases
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• Anyons from non-solvable finite groups are sufficient for universal quantum computation
• Sliding Phases in XY-Models, Crystals, and Cationic Lipid-DNA Complexes
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Boson Condensation in Topologically Ordered Quantum Liquids
• Quantum symmetries in discrete gauge theories
• Coupled wire construction of chiral spin liquids
• Quasi-Quantum Groups, Knots, Three-Manifolds, and Topological Field Theory
• Sliding Phases via Magnetic Fields
• Non-Abelian topological insulators from an array of quantum wires
• Chiral Spin Liquids in Arrays of Spin Chains
• Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
• Clifford Gates by Code Deformation
• Quantum Spin Hall Effect in Strip of Stripes Model
• Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems
• Topological Superconducting Phases of Weakly Coupled Quantum Wires
• Synthetic Topological Degeneracy by Anyon Condensation
• Composite Dirac liquids: parent states for symmetric surface topological order
• Pairing in Luttinger Liquids and Quantum Hall States
• $U(1)\times U(1)⋊Z_2$ Chern-Simons Theory and Z_4 Parafermion Fractional Quantum Hall States
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Integer and Fractional Quantum Hall Effect in a Strip of Stripes
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• A Crossed Sliding Luttinger Liquid Phase
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
• Wire constructions of Abelian topological phases in three or more dimensions
• Fibonacci Topological Superconductor
• Anyons in discrete gauge theories with Chern-Simons terms
• From an array of quantum wires to three-dimensional fractional topological insulators
• Fractional topological phases in three-dimensional coupled-wire systems
• Particle-hole symmetry and composite fermions in fractional quantum Hall states
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall states
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Phase transitions in Z_N gauge theory and twisted Z_N topological phases
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Quantum Hall hierarchy from coupled wires
• Two dimensional spin liquids with ${\mathbb{Z}}_2$ topological order in an array of quantum wires
• On Metaplectic Modular Categories and their applications
• Non-diagonal anisotropic quantum Hall states
• Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
• A non-Abelian twist to integer quantum Hall states
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Josephson Coupled Moore-Read States
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• From orbifolding conformal field theories to gauging topological phases
• Fractonic topological phases from coupled wires
• Translation symmetry-enriched toric code insulator
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States
• Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Paired parton quantum Hall states: a coupled wire construction
• Cloning SO(N) level 2
• Topological symmetry breaking: Domain walls and partial instability of chiral edges
• A coupled wire description of surface $ADE$ topological orders
• Topologically Induced Fermion Parity Flips in Superconductor Vortices
• Gauging Defects in Quantum Spin Systems

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