Persistence of gaps in the interacting Hofstadter model

Abstract

The energy spectrum of the Hofstadter model has a fractal structure with infinitely many gaps. We prove the persistence of each gap in presence of Hubbard interaction in the case of small transversal hopping, even when the coupling is much larger than the non interacting gaps. The proof relies on a subtle interplay of Renormalization Group arguments combined with number-theoretic properties of the incommensurate frequencies.

9 pages, 4 figures

References in corpus (7)

• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Spectral signatures of many-body localization with interacting photons
• Interaction instability of localization in quasiperiodic systems
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• The quasi-periodic quantum Ising transition in 1D
• Hofstadter butterfly for a finite correlated system

Cited by in corpus (7)

• Topological spin excitations in Harper-Heisenberg spin chains
• Stability of Weyl semimetals with quasiperiodic disorder
• Quantization of the interacting Hall conductivity in the critical regime
• Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
• Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
• Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model
• Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder