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

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

2010-09-13

arxiv.org/abs/1009.2360v2

J. Phys. A: Math. Theor. (Fast Track Communication) 43, 492002 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

13 pages, 4 figures

Scientific paper

10.1088/1751-8113/43/49/492002

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.

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