Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators

Abstract

Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here we demonstrate through numerical calculations on model wave functions that FCIs possess a fractionally quantized electric polarization, ${\vec{\mathcal{P}}}_{\text{o}}$, where $\text{o}$ is a high symmetry point. ${\vec{\mathcal{P}}}_{\text{o}}$ takes fractional values as compared to the allowed values for integer Chern insulators because of the possibility that anyons carry fractional quantum numbers under lattice translation symmetries. ${\vec{\mathcal{P}}}_{\text{o}}$, together with the discrete shift ${\mathcal{S}}_{\text{o}}$, determine fractionally quantized universal contributions to electric charge in regions containing lattice disclinations, dislocations, boundaries, and/or corners, and which are fractions of the minimal anyon charge. We demonstrate how these invariants can be extracted using Monte Carlo computations on model wave functions with lattice defects for 1/2-Laughlin and 1/3-Laughlin FCIs on the square and honeycomb lattice, respectively, obtained using the parton construction. These results comprise a class of fractionally quantized response properties of topologically ordered states that go beyond the known ones discovered over thirty years ago.

arXiv comment13 pages, 8 figures

References in corpus (36)

• Topological Photonics
• Symmetry protected topological orders and the group cohomology of their symmetry group
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Topological orders and Edge excitations in FQH states
• Quantum Orders and Symmetric Spin Liquids
• Nearly-flat bands with nontrivial topology
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Fractional Chern Insulator
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Fractional Quantum Hall Physics in Topological Flat Bands
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• 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
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Projective Construction of Non-Abelian Quantum Hall Liquids
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Parton construction of a wave function in the anti-Pfaffian phase
• Imaging moiré deformation and dynamics in twisted bilayer graphene
• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Fermionic symmetry fractionalization in (2+1)D
• Moire pattern as a magnifying glass for strain and dislocations in van der Waals heterostructures
• Fractional disclination charge and discrete shift in the Hofstadter butterfly
• Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Measuring strain and rotation fields at the dislocation core in graphene
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators

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• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators