Sufficient Conditions for Topological Order in Insulators

Abstract

We prove the existence of low energy excitations in insulating systems at general filling factor under certain conditions, and discuss in which cases these may be identified as topological excitations. This proof is based on previously proven locality results. In the case of half-filling it provides a significantly shortened proof of the recent higher dimensional Lieb-Schultz-Mattis theorem.

7 pages, no figures

References in corpus (1)

• Locality in Quantum and Markov Dynamics on Lattices and Networks

Cited by in corpus (69)

• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Solving Gapped Hamiltonians Locally
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Fractionalization, topological order, and quasiparticle statistics
• A Quantum Dipolar Spin Liquid
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl${}_3$ and Crystalline Spin-Orbital Liquids
• Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model
• Constraints on topological order in Mott Insulators
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Topological order from quantum loops and nets
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Real-space recipes for general topological crystalline states
• Dynamics at and near conformal quantum critical points
• Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling
• Spin Hamiltonians with resonating-valence-bond ground states
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• Dyonic Lieb-Shultz-Mattis Theorem and Symmetry Protected Topological Phases in Decorated Dimer Models
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Quantum many-body topology of quasicrystals
• Lieb-Schultz-Mattis theorems for symmetry protected topological phases
• Luttinger's theorem in presence of Luttinger surfaces
• Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
• Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice
• Featureless quantum insulator on the honeycomb lattice
• Landau-Forbidden Quantum Criticality in Rydberg Quantum Simulators
• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Stability of the spin-$1/2$ kagome ground state with breathing anisotropy
• The Lieb-Schultz-Mattis-type filling constraints in the 1651 magnetic space groups
• Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity
• Fermi Surface Symmetric Mass Generation
• Intrinsically Interacting Higher-Order Topological Superconductors
• (SPT-)LSM theorems from projective non-invertible symmetries
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• $\mathrm{SU}(4)$-Symmetric Quantum Spin-Orbital Liquids on Various Lattices
• Lieb-Schultz-Mattis theorem with a local twist for general one-dimensional quantum systems
• Lieb-Schultz-Mattis theorem for quasi-topological systems
• Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
• Fibonacci topological order from quantum nets
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Odd Fracton Theories, Proximate Orders, and Parton Constructions
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions
• Unconventional quantum phase transitions in a one-dimensional Lieb-Schultz-Mattis system
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Holographic models of non-Fermi liquid metals revisited: an effective field theory approach
• Filling constraints on translation invariant dipole conserving systems
• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases
• Electronic polarization in non-Bloch band theory
• Self-$G$-ality in 1+1 dimensions
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Topological 'Luttinger' invariants protected by non-symmorphic symmetry in semimetals
• Topological phases of non-symmorphic crystals : Shastry-Sutherland lattice at integer filling
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Possible phases of the spin-$1/2$ $XXZ$ model on a honeycomb lattice by boson-vortex duality
• Anisotropy-induced spin parity effects
• Geometric Effects on Tunneling in Driven Quantum Systems