Composite Weyl semimetal as a parent state for three dimensional topologically ordered phases

Abstract

We introduce (3+1) dimensional models of short-range-interacting electrons that form a strongly correlated many-body state whose low-energy excitations are relativistic neutral fermions coupled to an emergent gauge field, ${\text{QED}}_4$. We discuss the properties of this critical state and its instabilities towards exotic phases such as a gapless `composite' Weyl semimetal and fully gapped topologically ordered phases that feature anyonic point-like as well as line-like excitations. These fractionalized phases describe electronic insulators. They may be further enriched by symmetries which results in the formation of non-trivial surface states.

arXiv comment13 pages, 3 figures

References in corpus (41)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Weyl Semimetal in a Topological Insulator Multilayer
• Periodic table for topological insulators and superconductors
• Experimental discovery of Weyl semimetal TaAs
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Discovery of a Weyl Fermion semimetal state in NbAs
• Recent developments in transport phenomena in Weyl semimetals
• Symmetry Protected Topological phases of Quantum Matter
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Is the Composite Fermion a Dirac Particle?
• Interacting fermionic topological insulators/superconductors in three dimensions
• Weyl superconductors
• Particle-Vortex Duality from 3d Bosonization
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Braiding statistics of loop excitations in three dimensions
• Dual Dirac liquid on the surface of the electron topological insulator
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Atomic Scale Visualization of Quantum Interference on a Weyl Semimetal Surface by Scanning Tunneling Microscopy/Spectroscopy
• Particle-vortex duality in topological insulators and superconductors
• Bosonization and Mirror Symmetry
• Nonsupersymmetric dualities from mirror symmetry
• Layer construction of 3D topological states and string braiding statistics
• Composite Dirac liquids: parent states for symmetric surface topological order
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• $S$-duality of $u(1)$ gauge theory with $\theta =\pi$ on non-orientable manifolds: Applications to topological insulators and superconductors
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Interlayer coherent composite Fermi liquid phase in quantum Hall bilayers
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Are There Topologically Charged States Associated with Quantum Electrodynamics ?

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• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Topological order in interacting semimetals
• Fermionic dualities with axial gauge fields
• An exactly soluble model for a fractionalized Weyl semimetal
• Microscopic theory of fractional excitations in gapless bilayer quantum Hall states: semi-quantized quantum Hall states
• Dynamical Effects from Anomaly: Modified Electrodynamics in Weyl Semimetal
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays