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QI: Fachverband Quanteninformation
QI 4: Quantum Manybody Systems (joint session QI/TT)
QI 4.11: Vortrag
Montag, 9. März 2026, 18:15–18:30, BEY/0245
An emerging generator of rotations for a 1- or many-particle Hofstadter problem on a lattice pierced by magnetic field — •Arabi Seshappan1,2, Tangi Morvan2, Alberto Nardin2, and Leonardo Mazza2 — 1Department of Physics, University of California, Merced, CA 95343, USA — 2Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France
Topological quantum computation is an exciting direction for development of fault-tolerant qubits—a quintessential example being manipulation of excitations in fractional quantum Hall (FQH) systems. As recent cold-atom and photonic experiments have realized few-particle FQH states in small lattices, and theoretical results have shown spectra of specific lattice sizes to exhibit exactly flat-bands in momentum space, we have theoretically studied similar FQH lattices for 1- and many-particle bosonic cases. Our construction is that of a two-dimensional (2D) square lattice, with nearest-neighbor hopping, pierced by a perpendicular, uniform magnetic field. We vary the magnetic field such that, for lattice edge length L, the flux per plaquette ranges between α = 1/L and α = 1/4, and analyze the resultant spectra. We have found that, for low energy levels, measurements of density are an excellent proxy for defining a gauge-invariant generator of rotations (GIGR) and can make order in the spectra. This removes any need for assumption of circular droplet invariance, and provides a useful characterization technique for cold-atom experiments.
Keywords: Fractional Quantum Hall Effect; Hofstadter Model