Next-nearest-neighbor-tunneling-induced symmetry breaking of Hofstadter’s butterfly spectrum for ultracold atoms on the honeycomb lattice. (English) Zbl 1236.82152
Summary: We study the spectrum of ultracold atoms on the honeycomb lattice under a constant effective magnetic field. In the tight-binding approximation, we derived the generalized Harper’s equations and numerically calculate the spectrum, which has a fractal structure. For the cases with and without the next-nearest-neighbor tunneling, the graphs of spectra have different symmetries. Comparing the symmetries of the graphs of spectra, we find that next-nearest-neighbor tunneling induces symmetry breaking of the graph of spectrum.
MSC:
| 82D80 | Statistical mechanics of nanostructures and nanoparticles |
| 82D15 | Statistical mechanics of liquids |
| 81V45 | Atomic physics |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 28A80 | Fractals |
| 81R40 | Symmetry breaking in quantum theory |
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