The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

TL;DR

This paper analyzes the elementary excitations in an exactly solvable Russian doll BCS model of superconductivity, revealing novel excited Cooper pairs with higher energy states and a new quantum number Q.

Contribution

It provides the first exact solution-based study of low energy excitations, uncovering excited Cooper pairs and their RG interpretation in the Russian doll BCS model.

Findings

Existence of excited Cooper pairs with higher energy

Introduction of a quantum number Q in Bethe ansatz equations

Connection between Q and renormalization group analysis

Abstract

The recently proposed Russian doll BCS model provides a simple example of a many body system whose renormalization group analysis reveals the existence of limit cycles in the running coupling constants of the model. The model was first studied using RG, mean field and numerical methods showing the Russian doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In this paper we use the recently discovered exact solution of this model to study the low energy spectrum. We find that, in addition to the standard quasiparticles, the electrons can bind into Cooper pairs that are different from those forming the condensate and with higher energy. These excited Cooper pairs can be described by a quantum number Q which appears in the Bethe ansatz equation and has a RG interpretation.