Hofstadter butterfly in the Falicov-Kimball model on some finite 2D lattices

Abstract

Spinless, interacting electrons on a finite size triangular lattice moving in an extremely strong perpendicular magnetic field are studied and compared with the results on a square lattice. Using a Falicov-Kimball model, the effects of the magnetic field, Coulomb correlation and finite system size on their energy spectrum are observed. It is possible to induce a gap in the spectrum by tuning the magnetic field even in the absence of correlation, though extra states appear in the gap due to finite size. An orbital current is calculated for both the square and triangular lattice with and without electron correlation. In the noninteracting limit, the bulk current shows several patterns, while the edge current shows oscillations with magnetic flux. The oscillations persist in the interacting limit for the square lattice but not for the triangular lattice. Using exact diagonalization techniques, the recursive structure of Hofstadter spectrum is examined with strong electronic correlations for different system sizes. Electronic correlation is found to suppress these extra states in the gap in some cases.

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Spatial quantum noise interferometry in expanding ultracold atom clouds
• Single-site-resolved measurement of the current statistics in optical lattices
• Quantum phases in mixtures of fermionic atoms
• Hofstadter butterfly for a finite correlated system
• Mixtures of fermionic atoms in an optical lattice
• Orbital Effects of Strong Magnetic Field on a 2-D Holstein Polaron

Cited by in corpus (5)

• Metal-Insulator Transition and Band Magnetism in the Spin-$1/2$ Falicov-Kimball Model on A Triangular Lattice with External Magnetic Field
• Exciton condensation in an extended spinless Falicov Kimball model in the presence of orbital magnetic fields
• Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model
• Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field
• Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential