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arXiv · 2310.09565

Chern numbers for the two-body Hofstadter-Hubbard butterfly

D. C. Alyuruk·M. Iskin
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Abstract

We analyze the two-body spectrum within the Hofstadter-Hubbard model on a square lattice through an exact variational ansatz and study the topological properties of its low-lying two-body bound-state branches. In particular we discuss how the Hofstadter-Hubbard butterfly of the two-body branches evolves as a function of onsite interactions and how to efficiently calculate their Chern numbers using the Fukui-Hatsugai-Suzuki approach. Our numerical results are fully consistent with the simple picture that appears in the strong-coupling limit, where the attraction between fermions forms a composite boson characterized by an effective hopping parameter and an effective magnetic-flux ratio.

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D. C. Alyuruk, M. Iskin. 2023-10-14. Chern numbers for the two-body Hofstadter-Hubbard butterfly. https://doi.org/10.1103/physrevb.109.035149

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