Pairing in 4-component fermion systems: the bulk limit of SU(4)-symmetric Hamiltonians

TL;DR

This paper demonstrates that in large SU(4)-symmetric fermion systems, the BCS approximation accurately describes the ground state and excitation gaps, despite complex pairing correlations.

Contribution

It shows that the BCS approximation remains valid in the thermodynamic limit for SU(4)-symmetric Hamiltonians within the SO(8) Richardson-Gaudin model.

Findings

BCS approximation accurately predicts ground state energy in large systems

Quasiparticle gaps are well-described by BCS theory

Collective excitations do not alter bulk energy or gaps

Abstract

Fermion systems with more than two components can exhibit pairing condensates of much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8) Richardson-Gaudin model with SU(4)-symmetric Hamiltonians, we show that the BCS approximation remains valid in the thermodynamic limit of large systems for describing the ground state energy and the canonical and quasiparticle excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of collective excitations, but these do not affect the bulk energy and quasiparticle gaps.