Flux-fusion anomaly test and bosonic topological crystalline insulators

Abstract

We introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry enriched topological (SET) phases. We focus on bosonic systems with Z2 topological order, and symmetry group of the form G = U(1) $⋊$ G', where G' is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems, but can occur at surfaces of d=3 symmetry protected topological (SPT) phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In some cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by non-trivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry, and to show that some fractionalization patterns cannot be extended to a consistent action of G' symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with non-trivial anomalies, including G = U(1) X Z2T and G = U(1) X Z2P, where Z2T and Z2P are time-reversal and d=2 reflection symmetry, respectively.

18+13 pages, 4 figures. Significant changes to introduction, and other changes to improve presentation. Title shortened

References in corpus (24)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Crystalline Insulators
• "Deconfined" quantum critical points
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• The space group classification of topological band insulators
• Identifying Topological Order by Entanglement Entropy
• 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
• Putting competing orders in their place near the Mott transition
• Symmetry fractionalization and twist defects
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Theory of interacting topological crystalline insulators
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice
• Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators
• Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• String flux mechanism for fractionalization in topologically ordered phases

Cited by in corpus (29)

• Zoo of quantum-topological phases of matter
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Topological phases protected by point group symmetry
• Gauging spatial symmetries and the classification of topological crystalline phases
• Exactly Solvable Models for Symmetry-Enriched Topological Phases
• Lattice Homotopy Constraints on Phases of Quantum Magnets
• Crystalline topological phases as defect networks
• Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
• Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
• Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions
• Rotation Symmetry-Protected Topological Phases of Fermions
• Quantum Paramagnet and Frustrated Quantum Criticality in a Spin-One Diamond Lattice Antiferromagnet
• Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Classification of symmetry fractionalization in gapped ${\mathbb{Z}}_2$ spin liquids
• Folding approach to topological orders enriched by mirror symmetry
• Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice
• Anomaly cascade in (2+1)D fermionic topological phases
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• Surface field theories of point group symmetry protected topological phases
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Computing Defects Associated to Bounded Domain Wall Structures: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ Case
• Anomalies and symmetry fractionalization in reflection-symmetric topological order
• Mirror anomaly in fermionic topological orders
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Crystalline invariants of fractional Chern insulators
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations