Exact solutions for pairing interactions

TL;DR

This paper reviews the historical development and recent advances in exact solutions of the BCS pairing Hamiltonian, emphasizing the Richardson-Gaudin models' applications in nuclear physics and quantum integrable systems.

Contribution

It provides a comprehensive review of the Richardson solution and its extensions, highlighting their significance in modern quantum physics research.

Findings

Historical overview of Richardson's exact solution

Recent developments in Richardson-Gaudin models

Applications in nuclear physics and quantum integrable systems

Abstract

The exact solution of the BCS pairing Hamiltonian was found by Richardson in 1963. While little attention was paid to this exactly solvable model in the remainder of the 20th century, there was a burst of work at the beginning of this century focusing on its applications in different areas of quantum physics. We review the history of this exact solution and discuss recent developments related to the Richardson-Gaudin class of integrable models, focussing on the role of these various models in nuclear physics.