Lieb-Schultz-Mattis Theorem and the Filling Constraint
arXiv:2104.09561 · doi:10.1007/s11005-021-01480-4
Abstract
Following recent developments in the classification of bosonic short-range entangled phases, we examine many-body quantum systems whose ground state fractionalization obeys the Lieb-Schultz-Mattis (LSM) theorem. We generalize the topological classification of such phases by LSM anomalies (arXiv:1907.08204) to take magnetic and non-symmorphic lattice effects into account, and provide direct computations of the LSM anomaly in specific examples. We show that the anomaly-free condition coincides with established filling constraints (arXiv:1705.09298, arXiv:1505.04193), and we also derived new ones on novel crystalline quantum systems.
arXiv comment24 pages, 7 figures (v2: fixed typos and amended Proposition III.2 | v3: reformatted some equations/expressions | v4: final published version)
References in corpus (43)
- Fault-tolerant quantum computation by anyons
- Unpaired Majorana fermions in quantum wires
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Periodic table for topological insulators and superconductors
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Lieb-Schultz-Mattis in Higher Dimensions
- Symmetry Fractionalization, Defects, and Gauging of Topological Phases
- Electron Localization in the Insulating State
- Models for gapped boundaries and domain walls
- Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
- Topological classification with additional symmetries from Clifford algebras
- Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
- Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
- Symmetric-Gapped Surface States of Fractional Topological Insulators
- Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
- Symmetry Protected Topological phases and Generalized Cohomology
- Lattice Homotopy Constraints on Phases of Quantum Magnets
- Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions
- Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
- Crystalline topological phases as defect networks
- Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
- Spectral Sum Rules and Magneto-Roton as Emergent Graviton in Fractional Quantum Hall Effect
- Classification and construction of higher-order symmetry protected topological phases of interacting bosons
- Hadronic corrections to - scattering at NNLO with space-like data
- Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
- Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
- Fractional Quantum Hall Effect in Weyl Semimetals
- Quantum many-body topology of quasicrystals
- Higher Categories and Topological Quantum Field Theories
- Necessary and Sufficient Conditions for the Validity of Luttinger's Theorem
- Quantum Hall Systems: Braid groups, composite fermions, and fractional charge
- Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
- Rational indices for quantum ground state sectors
- Revisiting instanton corrections to the Konishi multiplet
- Extended quantum field theory, index theory and the parity anomaly
- Crystallographic T-duality
- Topological Superconductors and Category Theory
- Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices
- Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence
- Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
- Invertible Topological Field Theories
- Index Theory and the Baum-Connes conjecture