Few-body bound states in the anyon-Hubbard model

• URL: http://arxiv.org/abs/2609.09125v2
• Date: Tue, 15 Sep 2026 11:47:37 GMT
• Title: Few-body bound states in the anyon-Hubbard model
• Abstract summary: Anyon-Hubbard model (AHM) can be formulated in terms of bosons featuring density-dependent Peierls phases.<n>We show theoretically that the AHM also hosts exact two-body bound states in the continuum (BICs) for arbitrary $neq 0$, and genuine three- and four-body bound states.
• Score: 0.44694550240499314
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum statistics in low-dimensional systems predicts anyonic particles with fractional exchange statistics which are neither that of bosons nor fermions. While anyons are typically found in two dimensions as excitations of topologically-ordered states of matter, anyon-like exchange statistics has also been discussed in one dimension, for instance, in the context of the anyon-Hubbard model (AHM), the physics of which has recently been observed in experiment [Kwan et al., arXiv:2306.01737; Dhar et al., arXiv:2412.21131; and Bakkali-Hassani et al., arXiv:2602.20421]. The AHM can be formulated in terms of bosons featuring density-dependent Peierls phases, described by a statistical phase angle $θ$, which controls asymmetric transport and the formation of dynamically bound pairs at finite momentum. Here, we show theoretically that the AHM also hosts exact two-body bound states in the continuum (BICs) for arbitrary $θ\neq 0$, and genuine three- and four-body bound states. Unlike conventional bound states stabilized by attractive (or repulsive) interactions, which are energetically localized with a large effective mass, these clusters here are bound by a purely kinematic mechanism endowing them with fast chiral transport properties. We provide a simple variational approximation to the three-body bound states and explain their binding mechanism. Moreover, we show that the signatures of three-body bound states in the AHM can be directly probed experimentally from the expansion dynamics starting from three localized particles.

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