Unexpected systematic degeneracy in a system of two coupled Gaudin models with homogeneous couplings

TL;DR

This paper uncovers a systematic degeneracy in a symmetric system of two coupled Gaudin models, revealing a large degenerate subspace linked to the system's inversion symmetry, with implications for quantum information processing.

Contribution

It identifies and constructs the full degenerate subspace in coupled Gaudin models and explores its relation to inversion symmetry, a novel insight in this context.

Findings

Systematic degeneracy between multiplets in coupled Gaudin models.

Degenerate subspace lies in the kernel of a specific commutator.

Degeneracy linked to inversion symmetry in the system.

Abstract

We report an unexpected systematic degeneracy between different multiplets in an inversion symmetric system of two coupled Gaudin models with homogeneous couplings, as occurring for example in the context of solid state quantum information processing. We construct the full degenerate subspace (being of macroscopic dimension), which turns out to lie in the kernel of the commutator between the two Gaudin models and the coupling term. Finally we investigate to what extend the degeneracy is related to the inversion symmetry of the system and find that indeed there is a large class of systems showing the same type of degeneracy.