Exactly Solvable Many-Body Calogero–Dunkl Systems with Dihedral Angular Crystal Fields

We introduce a class of exactly solvable many-body quantum systems combining Calogero–Moser interactions with dihedral angular crystal fields in two dimensions. The model describes NNN identical particles confined in a harmonic potential and interacting through inverse-square pairwise potentials along Cartesian directions, together with angular barriers arranged according to the dihedral group symmetry. By constructing Dunkl operators associated with a reducible reflection group structure, we demonstrate that the Hamiltonian can be mapped, on an invariant subspace, to a system of independent harmonic oscillators up to a coupling-dependent constant shift.

This algebraic reduction yields an explicit closed-form energy spectrum and ground-state wavefunction, characterized by a Jastrow-type factor encoding both pairwise and angular singularities, multiplied by a Gaussian envelope. The resulting ground state exhibits strong angular localization and nontrivial correlation properties reminiscent of fractional statistics in one-dimensional systems. We further analyze physical observables, including the one-body density matrix, dynamic structure factor, and thermodynamic functions, highlighting how the interplay between many-body correlations and discrete rotational symmetry manifests in measurable quantities.

The model provides a unified and exactly solvable framework that combines two distinct integrable structures—Calogero interactions and dihedral Dunkl symmetry—within a single Hamiltonian. Possible experimental realizations in ultracold atoms, optical lattices, and quantum Hall-type systems are discussed, suggesting that such systems may offer a platform to probe symmetry-driven many-body effects and engineered angular potentials.