Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pairwise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere, and the system of hyperradial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyperradial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyperradius $\ensuremath{\rho}$ is studied, and the universal logarithmic dependence $\ensuremath{\sim}{\mathrm{ln}}^{3}\phantom{\rule{0.2em}{0ex}}\ensuremath{\rho}$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $(2+1)$ -scattering length are calculated.Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pairwise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere, and the system of hyperradial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyperradial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyperradius $\ensuremath{\rho}$ is studied, and the universal logarithmic dependence $\ensuremath{\sim}{\mathrm{ln}}^{3}\phantom{\rule{0.2em}{0ex}}\ensuremath{\rho}$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $(2+1)$-scattering length are calculated.

arXiv:physics/0606013Physical Review AOct 11, 200642 citations

Universal Properties of the Four-Boson System in Two Dimensions

L. Platter, H.-W. Hammer, Ulf-G. Meißner

arXiv:cond-mat/0405660Few-Body SystemsNov 25, 200410 citations

Universal bound and scattering properties for two dipoles

Yujun Wang, Chris H. Greene

The bound state and low-energy scattering properties of two oriented dipoles are investigated for both bosonic and fermionic symmetries. Interestingly, a universal scaling emerges for the expectation value of the angular momentum for deeply bound two-dipole states. This scaling traces to the pendulum motion of two dipoles in the strong dipole regime. The low-energy scattering phase shifts of two dipoles also show universal behavior. These universal observations make connections to the scaling laws reported by Wang et al. [Phys. Rev. Lett. 106, 233201 (2011); Phys. Rev. Lett. 107, 233201 (2011)] for three dipoles.The bound state and low-energy scattering properties of two oriented dipoles are investigated for both bosonic and fermionic symmetries. Interestingly, a universal scaling emerges for the expectation value of the angular momentum for deeply bound two-dipole states. This scaling traces to the pendulum motion of two dipoles in the strong dipole regime. The low-energy scattering phase shifts of two dipoles also show universal behavior. These universal observations make connections to the scaling laws reported by Wang et al. [Phys. Rev. Lett. 106, 233201 (2011); Phys. Rev. Lett. 107, 233201 (2011)] for three dipoles.

arXiv:1112.4934Physical Review AFeb 10, 201214 citations

Three bosons in one dimension with short-range interactions

Nirav P. Mehta, James A. Shepard

Bulletin of the American Physical SocietyMay 19, 20050 citations

Four-body physics in low-dimensional bosons with three-body interaction

V. Polkanov, Orest Hryhorchak, V. Pastukhov

arXiv:2506.18043Annals of PhysicsMay 22, 20260 citations

Z3 quantum criticality in a spin- 12 chain model

P. Lecheminant, E. Orignac

The stability of the magnetization $m=1/3$ plateau phase of the $\mathrm{XXZ}$ spin- $\frac{1}{2}$ Heisenberg chain with competing interactions is investigated upon switching on a staggered transverse magnetic field. Within a bosonization approach, it is shown that the low-energy properties of the model are described by an effective two-dimensional $\mathrm{XY}$ model in a threefold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the $m=1/3$ plateau phase to a phase where the spins are polarized along the staggered magnetic field. The ${Z}_{3}$ critical properties of the transition are determined within the bosonization approach.The stability of the magnetization $m=1/3$ plateau phase of the $\mathrm{XXZ}$ spin-$\frac{1}{2}$ Heisenberg chain with competing interactions is investigated upon switching on a staggered transverse magnetic field. Within a bosonization approach, it is shown that the low-energy properties of the model are described by an effective two-dimensional $\mathrm{XY}$ model in a threefold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the $m=1/3$ plateau phase to a phase where the spins are polarized along the staggered magnetic field. The ${Z}_{3}$ critical properties of the transition are determined within the bosonization approach.

arXiv:cond-mat/0309345Physical Review BMay 7, 200415 citations

(2+1)

-scattering length are calculated.

The stability of the magnetization

m=1/3

plateau phase of the

\mathrm{XXZ}

spin-

\frac{1}{2}

Heisenberg chain with competing interactions is investigated upon switching on a staggered transverse magnetic field. Within a bosonization approach, it is shown that the low-energy properties of the model are described by an effective two-dimensional

\mathrm{XY}

model in a threefold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the

m=1/3

plateau phase to a phase where the spins are polarized along the staggered magnetic field. The

{Z}_{3}

critical properties of the transition are determined within the bosonization approach.