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

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.

36 pages, 12 figures

References in corpus (4)

• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Log-periodic behavior of finite size effects in field theories with RG limit cycles
• Integrability of the russian doll BCS model
• Renormalization group limit-cycles and field theories for elliptic S-matrices

Cited by in corpus (7)

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• Cooper pairs and exclusion statistics from coupled free-fermion chains
• Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models
• A quantum mechanical model of the Riemann zeros
• The Riemann zeros and the cyclic Renormalization Group
• On the Quantum Reconstruction of the Riemann zeros
• BCS model with asymmetric pair scattering: a non-Hermitian, exactly solvable Hamiltonian exhibiting generalised exclusion statistics