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Degenerate eigenvalues for Hamiltonians with no obvious symmetries

Steven S. Gubser·Robert K. Bradley
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Abstract

Certain Hamiltonians based on two coupled quantum mechanical spins exhibit degenerate eigenvalues despite having no obvious non-abelian symmetries. Operators acting to permute the degenerate states do not have a simple form when expressed as polynomials of the generators of rotations for the respective spins. As observed in [1], one such Hamiltonian helps explain resonances in the spin relaxation rate of optically pumped Rb_2, as a function of applied magnetic field. We give an explanation of why the degeneracies exist, based on properties of the commutator and anti-commutator of the Hamiltonian and its image under magnetic field reversal.

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Steven S. Gubser, Robert K. Bradley. 2004-10-25. Degenerate eigenvalues for Hamiltonians with no obvious symmetries. https://arxiv.org/abs/physics/0312118

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