Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model

Abstract

We study how the stability of the fractional quantum Hall effect (FQHE) is influenced by the geometry of band structure in lattice Chern insulators. We consider the Hofstadter model, which converges to continuum Landau levels in the limit of small flux per plaquette. This gives us a degree of analytic control not possible in generic lattice models, and we are able to obtain analytic expressions for the relevant geometric criteria. These may be differentiated by whether they converge exponentially or polynomially to the continuum limit. We demonstrate that the latter criteria have a dominant effect on the physics of interacting particles in Hofstadter bands in this low flux density regime. In particular, we show that the many-body gap depends monotonically on a band-geometric criterion related to the trace of the Fubini-Study metric.

[v2] improved presentation; 11 pages, 5 figures

References in corpus (13)

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• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Berry Curvature and Quantum Metric in $N$-band systems -- an Eigenprojector Approach
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• Steady-state Hall response and quantum geometry of driven-dissipative lattices
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
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• Higher vortexability: zero field realization of higher Landau levels
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge
• Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
• Geometric bound on structure factor
• Superconductivity in a Topological Lattice Model with Strong Repulsion
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• Detecting Hidden Order in Fractional Chern Insulators
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• Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements
• Particles as superoscillations of spacetime with a nonlocal metric?
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Quantum mechanics as an approximated model: A geometrodynamical approach