Crystalline invariants of fractional Chern insulators
arXiv:2405.17431 · doi:10.1103/8bpm-qbzp
Abstract
In the presence of crystalline symmetry, topologically ordered states can acquire a host of symmetry-protected invariants. These determine the patterns of crystalline symmetry fractionalization of the anyons in addition to fractionally quantized responses to lattice defects. Here we show how ground state expectation values of partial rotations centered at high symmetry points can be used to extract crystalline invariants. Using methods from conformal field theory and G-crossed braided tensor categories, we develop a theory of invariants obtained from partial rotations, which apply to both Abelian and non-Abelian topological orders. We then perform numerical Monte Carlo calculations for projected parton wave functions of fractional Chern insulators, demonstrating remarkable agreement between theory and numerics. For the topological orders we consider, we show that the Hall conductivity, filling fraction, and partial rotation invariants fully characterize the crystalline invariants of the system. Our results also yield invariants of continuum fractional quantum Hall states protected by spatial rotational symmetry.
arXiv comment17 pages, 7 figures. minor edits
References in corpus (59)
- Topological Insulators
- Classification of topological quantum matter with symmetries
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Topological quantum chemistry
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Quantum Orders and Symmetric Spin Liquids
- Nearly-flat bands with nontrivial topology
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Topological classification of crystalline insulators through band structure combinatorics
- Identifying Topological Order by Entanglement Entropy
- Fractional Chern Insulator
- Symmetry Fractionalization, Defects, and Gauging of Topological Phases
- Fractional Quantum Hall Physics in Topological Flat Bands
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
- Observation of fractional Chern insulators in a van der Waals heterostructure
- Fractional Quantum Hall Effect in Optical Lattices
- Topological Nematic States and Non-Abelian Lattice Dislocations
- Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
- Topological order, emergent gauge fields, and Fermi surface reconstruction
- Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
- Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
- Topological phases protected by point group symmetry
- Building crystalline topological phases from lower-dimensional states
- Gauging spatial symmetries and the classification of topological crystalline phases
- Fractional disclination charge in two-dimensional symmetric topological crystalline insulators
- Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
- Projective Construction of Non-Abelian Quantum Hall Liquids
- Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
- Crystalline topological phases as defect networks
- Shift insulators: rotation-protected two-dimensional topological crystalline insulators
- Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
- Many-body Chern number from statistical correlations of randomized measurements
- Chiral central charge from a single bulk wave function
- Classification of (2+1)D invertible fermionic topological phases with symmetry
- Real-space recipes for general topological crystalline states
- Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
- Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
- Dislocation charges reveal two-dimensional topological crystalline invariants
- Spectroscopic signatures of crystal momentum fractionalization
- Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
- Extraction of many-body Chern number from a single wave function
- Detecting crystal symmetry fractionalization from the ground state: Application to spin liquids on the kagome lattice
- Comment on "Spin Transport properties of the quantum one-dimensional non-linear sigma model"
- Fractional disclination charge and discrete shift in the Hofstadter butterfly
- Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
- Measuring space-group symmetry fractionalization in Z spin liquids
- Flux-fusion anomaly test and bosonic topological crystalline insulators
- Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies
- Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
- Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
- Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
- Extracting higher central charge from a single wave function
- Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups