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Physics Letters A

Next-nearest-neighbor-tunneling-induced symmetry breaking of Hofstadter's butterfly spectrum for ultracold atoms on the honeycomb lattice

Jing-Min Hou, Wen‐Xing Yang

Published May 23, 2009• 8 citations
Publisher
DOI
10.1016/j.physleta.2009.05.045

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The light-matter interactions for an emitter coupling to the bulk region of a Hofstadter lattice were recently investigated by De Bernardis et al. [Phys. Rev. Lett. 126, 103603 (2021)]. We propose light-matter interactions in an extended Hofstadter lattice with the next-nearest-neighbor (NNN) couplings. Compared with the standard Hofstadter lattice, the NNN couplings break the mirror symmetry and the energy bands are not flat, but are dispersive with nonzero group velocity. In contrast to the study by De Bernardis et al., when a two-level emitter interacts with the bulk region of the extended Hofstadter lattice, the emitter is no longer trapped by the coherent oscillations and can radiate photons unidirectionally. The chiral mechanism stems from the broken mirror symmetry. Both the radiation rate and the chirality periodically change with the emitter's coupling position. All of those particular features can be realized on the photonic lattice platform and may find potential application in chiral quantum information processing.
We study the revival of Hofstadter butterfly due to the competition between disorder and electronic interaction using mean field approximation of unrestricted Hartree Fock method at zero temperature for two dimensional square and honeycomb lattices. Interplay of disorder and electronic correlation to nullify each other is corroborated by the fact that honeycomb lattice needs more strength of electronic correlation owing to its less co-ordination number which enhances the effect of disorder. The extent of revival of the butterfly is better in square lattice than honeycomb lattice due to higher coordination number. The effect of disorder and interaction is also investigated to study entanglement entropy and entanglement spectrum. We find that for honeycomb lattice area law of entanglement entropy is obeyed in all cases but for square lattice there is some departure from area law for larger subsystems. The entanglement spectrum have the reflection symmetry of the original butterfly of the Hofstadter spectrum. The interaction induces a gap in the entanglement spectrum as well conforming the correspondence between physical spectrum and entanglement spectrum. The effect of disorder closes the interaction induced gap in the entanglement spectrum establishing the nullification of interaction due to disorder and vice versa.