Boson topological insulators: A window into highly entangled quantum phases

Abstract

We study several aspects of the realization of global symmetries in highly entangled phases of quantum matter. Examples include gapped topological ordered phases, gapless quantum spin liquids and non-fermi liquid phases. An insightful window into such phases is provided by recent developments in the theory of short ranged entangled Symmetry Protected Topological (SPT) phases . First they generate useful no-go constraints on how global symmetry may be implemented in a highly entangled phase. Possible symmetry implementation in gapped topological phases and some proposed gapless spin/bose liquids are examined in this light. We show that some previously proposed spin liquid states for 2d quantum magnets do not in fact have consistent symmetry implementation unless they occur as the surface of a 3d SPT phase. A second SPT-based insight into highly entangled states is the development of a view point of such states as SPT phases of one of the emergent excitations. We describe this in the specific context of time reversal symmetric 3d U(1) quantum spin liquids with an emergent photon. Different such spin liquids are shown to be equivalent to different SPT insulating phases of the emergent monopole excitation of such phases. The highly entangled states also in turn enrich our understanding of SPT phases. We use the insights obtained from our results to provide an explicit construction of bosonic SPT phases in 3d in a system of coupled layers. This includes construction of a time reversal symmetric SPT state that is not currently part of the cohomology classification of such states.

17 pages, 1 figure

References in corpus (11)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A classification of symmetry enriched topological phases with exactly solvable models
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Three dimensional resonating valence bond liquids and their excitations
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Spin-charge Separated Solitons in a Topological Band Insulator
• Spin Charge Separation in the Quantum Spin Hall State
• Symmetry protected Spin Quantum Hall phases in 2-Dimensions
• Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice
• A K matrix Construction of Symmetry Enriched Phases of Matter

Cited by in corpus (161)

• Classification of topological quantum matter with symmetries
• Zoo of quantum-topological phases of matter
• Symmetry Protected Topological phases of Quantum Matter
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Interacting topological insulators: a review
• Deconfined quantum critical points: symmetries and dualities
• Interacting fermionic topological insulators/superconductors in three dimensions
• Classification of interacting electronic topological insulators in three dimensions
• Symmetry protected topological phases from decorated domain walls
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Topological phases protected by point group symmetry
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Choreographed entangle dances: topological states of quantum matter
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Dual Dirac liquid on the surface of the electron topological insulator
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• Topological phases with generalized global symmetries
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• A theory of 2+1D bosonic topological orders
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Anomalous Symmetry Fractionalization and Surface Topological Order
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Exactly Solvable Models for Symmetry-Enriched Topological Phases
• Average Symmetry-Protected Topological Phases
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Layer construction of 3D topological states and string braiding statistics
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Symmetric Mass Generation
• Composite fermi liquids in the lowest Landau level
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Time-reversal symmetric U(1) quantum spin liquids
• Bosonic topological phases of matter: bulk-boundary correspondence, SPT invariants and gauging
• Symmetry protected topological order at nonzero temperature
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Anomalies and Symmetry Fractionalization
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Anomaly indicators for time-reversal symmetric topological orders
• Microscopic model for the boson integer quantum Hall effect
• Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases
• Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Universal symmetry-protected topological invariants for symmetry-protected topological states
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Real-space recipes for general topological crystalline states
• Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation
• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases
• Minimalist approach to the classification of symmetry protected topological phases
• Composite fermion duality for half-filled multicomponent Landau Levels
• Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Bosonic integer quantum Hall effect in optical flux lattices
• Anomalous Symmetries End at the Boundary
• A simple anisotropic three-dimensional quantum spin liquid with fracton topological order
• Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D
• Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
• Relative Anomalies in (2+1)D Symmetry Enriched Topological States
• Wire constructions of Abelian topological phases in three or more dimensions
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Fractional topological phases in three-dimensional coupled-wire systems
• All-fermion electrodynamics and fermion number anomaly inflow
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• Symmetry-protected self-correcting quantum memories
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• A gauge theory generalization of the fermion-doubling theorem
• Realizing topological surface states in a lower-dimensional flat band
• Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions
• Bosonic topological insulator intermediate state in the superconductor-insulator transition
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Symmetry enriched U(1) quantum spin liquids
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1D
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Quantum Paramagnet and Frustrated Quantum Criticality in a Spin-One Diamond Lattice Antiferromagnet
• Flux-fusion anomaly test and bosonic topological crystalline insulators
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Detecting Majorana fermions in quasi-one-dimensional topological phases using nonlocal order parameters
• Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries $G_f$ and in any dimensions
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Classification of symmetry fractionalization in gapped ${\mathbb{Z}}_2$ spin liquids
• Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
• Interacting surface states of three-dimensional topological insulators
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• String flux mechanism for fractionalization in topologically ordered phases
• Unwinding Short-Range Entanglement
• Two dimensional Symmetry Protected Topological Phases with PSU(N) and time reversal symmetry
• Bosonic Crystalline Symmetry Protected Topological Phases Beyond the Group Cohomology Proposal
• Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Walker-Wang models and axion electrodynamics
• Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
• Folding approach to topological orders enriched by mirror symmetry
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases
• Anomalous symmetry protected topological states in interacting fermion systems
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points
• Condensations in higher categories
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Boundary RG Flows for Fermions and the Mod 2 Anomaly
• An infinite family of 3d Floquet topological paramagnets
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• $Z_2$ fractionalized Chern/topological insulators in an exactly soluble correlated model
• (3+1)D topological orders with only a ${\mathbb{Z}}_2$-charged particle
• Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories
• Fractionalization of subsystem symmetries in two dimensions
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Fractionalizing Global Symmetry on Looplike Topological Excitations
• Squeezing-induced Topological Gap Opening on Bosonic Bogoliubov Excitations
• Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries
• Edge theories of 2D fermionic symmetry protected topological phases protected by unitary Abelian symmetries
• Localized surfaces of three dimensional topological insulators
• Quasiparticle Berry curvature and Chern numbers in spin-orbit coupled bosonic Mott insulators
• Average-exact mixed anomalies and compatible phases
• Categories of quantum liquids II
• Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Fractionalized gapless quantum vortex liquids
• Enforced symmetry breaking by invertible topological order
• Topological quantum criticality from multiplicative topological phases
• Bound states of three fermions forming symmetry-protected topological phases
• Fake gaps in AdS_3/CFT_2
• Mirror anomaly in fermionic topological orders
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Edge Theories for Anyon Condensation Phase Transitions
• The Weyl-Mott point: topological and non-Fermi liquid behavior from an isolated Green's function zero
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Fermionic defects of topological phases and logical gates
• Boundary condition and reflection anomaly in $2+1$ dimensions
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries