Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids

Abstract

Topological crystalline insulators (TCIs) are nontrivial quantum phases of matter protected by crystalline (and other) symmetries. They are originally predicted by band theories, so an important question is their stability under interactions. In this paper, by directly studying the physical bulk properties of several band-theory-based nontrivial TCIs that are conceptually interesting and/or experimentally feasible, we show they are stable under interactions. These TCIs include (1) a weak topological insulator, (2) a TCI with a mirror symmetry and its time-reversal symmetric generalizations, (3) a doubled topological insulator with a mirror symmetry, and (4) two TCIs with symmetry-enforced-gapless surfaces. We describe two complementary methods that allow us to determine the properties of the magnetic monopoles obtained by coupling these TCIs to a U(1) gauge field. These methods involve studying different types of surface states of these TCIs. Applying these methods to our examples, we find all of them have nontrivial monopoles, which proves their stability under interactions. Furthermore, we discuss two levels of relations between these TCIs and symmetry enriched U(1) quantum spin liquids (QSLs). First, these TCIs are directly related to U(1) QSLs with crystalline symmetries. Second, there is an interesting correspondence between U(1) QSLs with crystalline symmetries and U(1) QSLs with internal symmetries. In particular, the TCIs with symmetry-enforced-gapless surfaces are related to the "fractional topological paramagnets" introduced in Ref. 1 by Zou et al.

arXiv comment10 pages + appendices + references

References in corpus (59)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Topological Field Theory of Time-Reversal Invariant Insulators
• Classification of topological quantum matter with symmetries
• Topological Crystalline Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Experimental realization of a topological crystalline insulator in SnTe
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Three-Dimensional Topological Insulators
• Inversion Symmetric Topological Insulators
• Hourglass Fermions
• Observation of Dirac node formation and mass acquisition in a topological crystalline insulator
• A classification of symmetry enriched topological phases with exactly solvable models
• Interacting fermionic topological insulators/superconductors in three dimensions
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Boson topological insulators: A window into highly entangled quantum phases
• Classification of interacting electronic topological insulators in three dimensions
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Stacked topological insulator built from bismuth-based graphene sheet analogues
• Topological phases protected by point group symmetry
• Classification and analysis of two dimensional abelian fractional topological insulators
• Building crystalline topological phases from lower-dimensional states
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Dual Dirac liquid on the surface of the electron topological insulator
• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Sub-nm wide electron channels protected by topology
• Symmetry fractionalization and twist defects
• Topological Insulators from Group Cohomology
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Theory of interacting topological crystalline insulators
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries
• Time-reversal symmetric U(1) quantum spin liquids
• Time-reversal symmetric hierarchy of fractional incompressible liquids
• A K matrix Construction of Symmetry Enriched Phases of Matter
• Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice
• Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry
• All-fermion electrodynamics and fermion number anomaly inflow
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Symmetry Enrichment in Three-Dimensional Topological Phases
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Stripe melting, a transition between weak and strong symmetry protected topological phases
• Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators
• Condensation of Lattice Defects and Melting Transitions in Quantum Hall phases
• Geometry defects in Bosonic symmetry protected topological phases

Cited by in corpus (23)

• Fracton-Elasticity Duality
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Pinch Point Singularities of Tensor Spin Liquids
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Field-induced QCD${}_3$-Chern-Simons quantum criticalities in Kitaev materials
• Symmetry enriched U(1) quantum spin liquids
• Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Intrinsically Interacting Higher-Order Topological Superconductors
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries
• Classification of symmetry-enriched topological quantum spin liquids
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices