Momentum-space Harper-Hofstadter model
arXiv:1411.1203 · doi:10.1103/PhysRevA.92.023609
Abstract
We show how the weakly trapped Harper-Hofstadter model can be mapped onto a Harper-Hofstadter model in momentum space. In this momentum-space model, the band dispersion plays the role of the periodic potential, the Berry curvature plays the role of an effective magnetic field, the real-space harmonic trap provides the momentum-space kinetic energy responsible for the hopping, and the trap position sets the boundary conditions around the magnetic Brillouin zone. Spatially local interactions translate into nonlocal interactions in momentum space: within a mean-field approximation, we show that increasing interparticle interactions leads to a structural change of the ground state, from a single rotationally symmetric ground state to degenerate ground states that spontaneously break rotational symmetry.
10 pages, 7 figures
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- Quantum Hall effect in momentum space
- Momentum-space Landau levels in driven-dissipative cavity arrays
- Interaction-induced chiral-transport inversion
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