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arXiv:2505.23255

Hierarchy of localized many-body bound states in an interacting open lattice

Yanxia Liu, Shu Chen

Published May 29, 2025• 0 citations
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Abstract

We unveil the mechanism for the formation of puzzled boundary-localized bound states in a spinless fermionic open lattice with nearest-neighbor interactions. By solving the Bethe-ansatz equation analytically, we uncover asymmetrical string solutions corresponding to the boundary-localized bound states, which emerge in systems with at least three particles. The localized bound states can become bound states in continuum in a suitable parameter region. When the number of particles increases to five or more, additional bound states away from the edge are also observed. Through rigorous analysis, we derive recurrence relations of the quasi-momentum of the localized states as a function of the number of particles, predicting the presence of hierarchy of localized many-body bound states in interacting open lattices.

DOI
10.48550/arxiv.2505.23255

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We consider a system of three particles consisting of two identical fermions and one other particle on a one-dimensional lattice. The fermions interact via a nearest-neighbor potential of strength μ1∈R\mu_1\in\mathbb{R}μ1​∈R , while the interaction between a fermion and one other particle is via an on-site potential with strength μ2∈R{\mu_2\in\mathbb{R}}μ2​∈R . We establish existence of bound states of the associated three-body lattice Schrödinger operator for all values of the total quasimomentum K∈T1K\in\mathbb{T}^1K∈T1 . Furthermore, we show that both the bound state fμ1μ2(K; ⋅ , ⋅ )f_{\mu_1\mu_2}(K;\,{\cdot}\,{,}\,{\cdot}\,)fμ1​μ2​​(K;⋅,⋅) and its corresponding eigenvalue Eμ1μ2(K)E_{\mu_1\mu_2}(K)Eμ1​μ2​​(K) depend holomorphically on the quasimomentum.
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