Exact quantum geometry from sublattice symmetry: Closed-form solution of the quarter-flux Harper-Hofstadter model

arXiv:2608.26099 · cond-mat.quant-gas, cond-mat.mes-hall, quant-ph · Submitted 2026-08-26 · Read on arXiv

cond-mat.quant-gas, cond-mat.mes-hall, quant-ph

Submitted: 2026-08-26

Updated: 2026-09-22

Terminology

• Berry Curvature — 51× in this paper · explained in 3 episodes
• Trace — 35× in this paper · explained in 2 episodes
• Chern Number — 19× in this paper · explained in 4 episodes
• MAGNETIC UNIT CELL — 14× in this paper
• Anisotropy — 5× in this paper · explained in 3 episodes
• Entanglement — 2× in this paper · explained in 3 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Hubbard Model — 2× in this paper · explained in 3 episodes
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Quantum Geometric Tensor (QGT) — 2× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Adiabatic Evolution — 1× in this paper · explained in 2 episodes
• Admissibility — 1× in this paper · explained in 2 episodes
• Arbitrary Superpositions — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Momentum transfer — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Floquet quantum geometry in periodically driven topological insulators
• Quantum Geometric Bounds in Non-Hermitian Systems
• Quaternion-K"ahler geometry of time reversal symmetric crystals
• Wilson-Loop-Ideal Bands and General Idealization
• Quantum geometry beyond projective single bands
• Second-Chern Bounds in Non-Abelian Quantum Geometry
• A Pfaffian quantum Hall state of ultracold bosons
• Ideal Bands in Tight-Binding Models
• Quantum-Geometric Design of Lattice Generalized Landau Levels
• Classification of fractional quantum Hall states with spatial symmetries

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