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.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.

arXiv:2505.23255May 29, 20250 citations

On the number of discrete levels in the quantum problem of three particles

Dimitri R. Yafaev

Theoretical and Mathematical PhysicsApr 1, 19767 citations

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

Yanxia Liu, Shu Chen

We unveil the mechanism of the puzzling boundary-localized bound states formation 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 (LBSs) can become bound states in continuum with a suitably chosen parameter. When the number of particles increases to five or more, additional LBSs away from the boundary are also observed. Through rigorous analysis, we derive recurrence relations of the quasimomentum of the localized states as a function of the number of particles, predicting the presence of a hierarchy of many-body LBSs in interacting open lattices.We unveil the mechanism of the puzzling boundary-localized bound states formation 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 (LBSs) can become bound states in continuum with a suitably chosen parameter. When the number of particles increases to five or more, additional LBSs away from the boundary are also observed. Through rigorous analysis, we derive recurrence relations of the quasimomentum of the localized states as a function of the number of particles, predicting the presence of a hierarchy of many-body LBSs in interacting open lattices.

Physical review. B./Physical review. BNov 4, 20251 citation

Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice

Mukhiddin Ishkobilovich Muminov

Theoretical and Mathematical PhysicsJul 1, 20104 citations

Bound states of strongly interacting three-body systems on a lattice

J. I. Abdullaev, Akhmad Miyassarovich Khalkhuzhaev, J. Kh. Boymurodov

Complex Analysis and Operator TheoryOct 24, 20252 citations

Exploring universal and nonuniversal regimes of trimers from three-body interactions in one-dimensional lattices

Arthur Christianen, John Sous

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbor two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\ensuremath{\le}\ensuremath{-}2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\ensuremath{\rightarrow}\ensuremath{\infty}$, while both sufficiently attractive $U$ and $V$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V\ensuremath{\gg}t,\phantom{\rule{0.16em}{0ex}}U<\ensuremath{-}2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbor two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\ensuremath{\le}\ensuremath{-}2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\ensuremath{\rightarrow}\ensuremath{\infty}$, while both sufficiently attractive $U$ and $V$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V\ensuremath{\gg}t,\phantom{\rule{0.16em}{0ex}}U<\ensuremath{-}2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.

arXiv:1806.10647Physical Review AJun 4, 20202 citations

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping

t

and and nearest-neighbor two-body

U

and three-body

V

interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\ensuremath{\le}\ensuremath{-}2t$ and positive

V>0

a large trimer is stabilized, which persists as $V\ensuremath{\rightarrow}\ensuremath{\infty}$, while both sufficiently attractive

U

and

V

bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V\ensuremath{\gg}t,\phantom{\rule{0.16em}{0ex}}U<\ensuremath{-}2t$ the bound-state behavior qualitatively evolves with larger

|U|

from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.