We study a model of three mutually interacting identical particles confined in a one-dimensional space, giving correlated states without one-body approximations. Certain types of quantum dynamics are illustrated with the model: quantum tunneling of position exchange and interparticle vibration (lattice vibration or phonons). The former is meaningful in the case that the identical particles are distinguished by their internal degrees of freedom. The unitary time evolution is simply written down in terms of the coherence of energy eigenfunctions. Our model clearly describes how the interparticle interaction divides one of the normal modes of the relative motion into tunneling and vibration of the particles.We study a model of three mutually interacting identical particles confined in a one-dimensional space, giving correlated states without one-body approximations. Certain types of quantum dynamics are illustrated with the model: quantum tunneling of position exchange and interparticle vibration (lattice vibration or phonons). The former is meaningful in the case that the identical particles are distinguished by their internal degrees of freedom. The unitary time evolution is simply written down in terms of the coherence of energy eigenfunctions. Our model clearly describes how the interparticle interaction divides one of the normal modes of the relative motion into tunneling and vibration of the particles.

Progress of Theoretical PhysicsJul 1, 20020 citations

Few-body bound states in the anyon-Hubbard model

Isaac Tesfaye, Christina Mascherbauer, Joyce Kwan +6 more

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.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.

cond-mat.quant-gasCross-listedarXiv:2609.09125Sep 9, 20260 citations

A model study of finite range three-body interactions

Rutgers University

Annals of PhysicsMay 1, 19900 citations

Contact Interaction Model for Three-Body Systems

D. V. Fedorov, A. S. Jensen

Few-Body SystemsMay 1, 20023 citations

Composite Particles in Many-Body Theory

Wesley E. Brittin, A.Y. Sakakura

Springer eBooksJan 1, 19741 citation

Fluctuation-exchange theory for general lattice Hamiltonians

Gökhan Esirgen, N. E. Bickers

The fluctuation-exchange, or FLEX, approximation for interacting electrons is derived for lattice Hamiltonians with general instantaneous one- and two-body terms. The use of a two-body basis set indexed by relative separation, rather than relative momentum, is emphasized. The fluctuation-exchange approximation for the three-orbital ${\mathrm{CuO}}_{2}$ model with on-site and near-neighbor Coulomb interactions is solved for one-particle properties. Unit-cell densities corresponding to both ``hole doping'' and ``electron doping'' are studied. The model is found to be far from a charge-density instability for all reasonable parameter values. The only nearly unstable particle-hole channel for unit-cell densities close to unity has Q\ensuremath{\sim}(\ensuremath{\pi},\ensuremath{\pi}) and S=1 (antiferromagnetic). The Fermi surface of the interacting system is computed, and the Luttinger theorem verified numerically in its most general context. Orbital-projected occupancy factors and spectral densities are examined.The fluctuation-exchange, or FLEX, approximation for interacting electrons is derived for lattice Hamiltonians with general instantaneous one- and two-body terms. The use of a two-body basis set indexed by relative separation, rather than relative momentum, is emphasized. The fluctuation-exchange approximation for the three-orbital ${\mathrm{CuO}}_{2}$ model with on-site and near-neighbor Coulomb interactions is solved for one-particle properties. Unit-cell densities corresponding to both ``hole doping'' and ``electron doping'' are studied. The model is found to be far from a charge-density instability for all reasonable parameter values. The only nearly unstable particle-hole channel for unit-cell densities close to unity has Q\ensuremath{\sim}(\ensuremath{\pi},\ensuremath{\pi}) and S=1 (antiferromagnetic). The Fermi surface of the interacting system is computed, and the Luttinger theorem verified numerically in its most general context. Orbital-projected occupancy factors and spectral densities are examined.

Physical review. B, Condensed matterJan 15, 199742 citations

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.

{\mathrm{CuO}}_{2}

model with on-site and near-neighbor Coulomb interactions is solved for one-particle properties. Unit-cell densities corresponding to both ``hole doping'' and ``electron doping'' are studied. The model is found to be far from a charge-density instability for all reasonable parameter values. The only nearly unstable particle-hole channel for unit-cell densities close to unity has Q\ensuremath{\sim}(\ensuremath{\pi},\ensuremath{\pi}) and S=1 (antiferromagnetic). The Fermi surface of the interacting system is computed, and the Luttinger theorem verified numerically in its most general context. Orbital-projected occupancy factors and spectral densities are examined.