A Quantum Many-body Problem in Two Dimensions: Ground State

TL;DR

This paper derives the exact ground state for a two-dimensional quantum many-body problem, linking it to random matrix theory, and analyzes its properties including energy and correlations.

Contribution

It provides the first exact solution for the 2D Calogero-Sutherland model and connects it to complex random matrix ensembles.

Findings

Ground state energy calculated in the thermodynamic limit

Pair-correlation function characterized showing no long-range order

Connection established between the quantum problem and complex matrix random matrices

Abstract

We obtain the exact ground state for the Calogero-Sutherland problem in arbitrary dimensions. In the special case of two dimensions, we show that the problem is connected to the random matrix problem for complex matrices, provided the strength of the inverse-square interaction $g = 2$. In the thermodynamic limit, we obtain the ground state energy and the pair-correlation function and show that in this case there is no long-range order.