Ideal Chern bands are Landau levels in curved space

Abstract

We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a non-uniform magnetic field. In addition, we design an operational test for the most general instance of such lowest Landau level mapping, which only relies on the computationally inexpensive evaluation of Bloch wavefunctions' derivatives. Our work clarifies the common origin of various Chern-idealness criteria, proves that these criteria exhaust all possible lowest Landau levels, and hints at classes of Chern bands that may posses interesting phases beyond Landau level physics.

8 pages

References in corpus (21)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Fractional quantum Hall effect in the absence of Landau levels
• Anyons and the quantum Hall effect - a pedagogical review
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Chiral model of twisted bilayer graphene realized in a monolayer
• The "forgotten" pseudomomenta and gauge changes in generalized Landau Level problems: spatially nonuniform magnetic and temporally varying electric fields
• Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices

Cited by in corpus (32)

• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
• Sublattice structure and topology in spontaneously crystallized electronic states
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Higher vortexability: zero field realization of higher Landau levels
• Bridging the small and large in twisted transition metal dicalcogenide homobilayers: a tight binding model capturing orbital interference and topology across a wide range of twist angles
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect
• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• Broken Symmetry in Ideal Chern Bands
• Universal Wilson Loop Bound of Quantum Geometry
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Emergent curved space and gravitational lensing in quantum materials
• Topologically protected flatness in chiral moiré heterostructures
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
• Anomalous Bilayer Quantum Hall Effect
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Quantum geometric tensors from sub-bundle geometry
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Quantum geometry, localization, and topological bounds of spin fluctuations
• Robustness of real-space topology in moiré systems
• Instability of Laughlin FQH liquids into gapless power-law correlated states with continuous exponents in ideal Chern bands: rigorous results from plasma mapping
• Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
• Two dimensional sub-wavelength topological dark state lattices