Fractional Chern insulators with a non-Landau level continuum limit

Abstract

Recent developments in fractional quantum Hall (FQH) physics highlight the importance of studying FQH phases of particles partially occupying energy bands that are not Landau levels. FQH phases in the regime of strong lattice effects, called fractional Chern insulators, provide one setting for such studies. As the strength of lattice effects vanishes, the bands of generic lattice models asymptotically approach Landau levels. In this article, we construct lattice models for single-particle bands that are distinct from Landau levels even in this continuum limit. We describe how the distinction between such bands and Landau levels is quantified by band geometry over the magnetic Brillouin zone and reflected in the electromagnetic response. We analyze the localization-delocalization transition in one such model and compute a localization length exponent of 2.57(3). Moreover, we study interactions projected to these bands and find signatures of bosonic and fermionic Laughlin states. Most pertinently, our models allow us to isolate conditions for optimal band geometry and gain further insight into the stability of FQH phases on lattices.

19 pages, 13 figures

References in corpus (24)

• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Flat Bands in Slightly Twisted Bilayer Graphene
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Critical exponent for the quantum Hall transition
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Quantum Metric and Correlated States in Two-dimensional Systems
• Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Topological Lattice Models with Constant Berry Curvature
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• "Hall viscosity" and intrinsic metric of incompressible fractional Hall fluids
• Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition
• Integer quantum Hall transition in a $\text{fraction}$ of a Landau level
• Geometric scaling in the quantum Hall system
• Numerical Study of a Dual Representation of the Integer Quantum Hall Transition
• Green's functions on a renormalized lattice: An improved method for the integer quantum Hall transition
• Elliptic mirror of the quantum Hall effect

Cited by in corpus (18)

• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Quantum Metric Induced Phases in Moiré Materials
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Recent Developments in Fractional Chern Insulators
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Local geometry and quantum geometric tensor of mixed states
• Drude weight and the many-body quantum metric in one-dimensional Bose systems
• Dissipation Induced Flat Bands
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
• Flat Bands and High Chern Numbers in Twisted Multilayer Graphene
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
• Localization renormalization and quantum Hall systems
• Quantum Geometric Tensor for Mixed States Based on the Covariant Derivative
• Evolution of quantum geometric tensor of 1D periodic systems after a quench