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arXiv · 1309.6329

Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

Shintaro Takayoshi·Hosho Katsura·Noriaki Watanabe·Hideo Aoki
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Abstract

To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $π$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising it pairs of bosons. Interestingly, the high- and low- density regions have an overlap, where the two phases coexist.

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Shintaro Takayoshi, Hosho Katsura, Noriaki Watanabe, Hideo Aoki. 2013-12-09. Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands. https://doi.org/10.1103/physreva.88.063613

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