What are the elementary excitations of the BCS model in the canonical ensemble?

TL;DR

This paper identifies the elementary excitations of the exactly solvable BCS model with fixed particle number, revealing unique dispersion relations and counting properties, and connects them to an effective Gaudin model for large systems.

Contribution

It provides the first detailed analysis of elementary excitations in the canonical ensemble BCS model, including a novel counting algorithm and graphical interpretation.

Findings

Excitations have peculiar dispersion relations with no Bogoliubov counterparts.

An algorithm for counting excitations in each excited state is developed.

Large system behavior is described by an effective Gaudin model.

Abstract

We have found the elementary excitations of the exactly solvable BCS model for a fixed number of particles. These turn out to have a peculiar dispersion relation, some of them with no counterpart in the Bogoliubov picture, and unusual counting properties related to an old conjecture made by Gaudin. We give an algorithm to count the number of excitations for each excited state and a graphical interpretation in terms of paths and Young diagrams. For large systems the excitations are described by an effective Gaudin model, which accounts for the finite size corrections to BCS.