Algorithms to solve the Sutherland model

TL;DR

This paper compares two algorithms for solving the Sutherland model, demonstrating their equivalence and providing insights into their differences and similarities in solving quantum many-body systems with specific interactions.

Contribution

It presents a detailed comparison and proof of equivalence between the classical Sutherland algorithm and a new limiting case algorithm for the elliptic generalization.

Findings

Both algorithms produce identical solutions.

The algorithms are equally simple despite differences.

The new algorithm extends understanding of elliptic generalizations.

Abstract

We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.