Novel correlations in two dimensions: Some exact solutions

TL;DR

This paper introduces a new two-dimensional many-body Hamiltonian with exact ground and excited states, revealing novel pairwise correlations and spectral properties akin to the Calogero-Sutherland model.

Contribution

It constructs an exactly solvable two-dimensional many-body model with unique correlations and spectral features, extending known one-dimensional integrable systems.

Findings

Exact ground state with novel pairwise correlations

Exact excited states with Calogero-Sutherland-like spectrum

Model reduces to a Sutherland-like system on a ring

Abstract

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring.