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Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

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Banaszak G., Barańczuk S., Lulek T., Milewski J., Stagraczyński R.
Acta Physica Polonica A
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2012
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vol. 121
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issue 5-6
1111-1114
EN
We analyse the number field-theoretic properties of solutions of the eigenproblem of the Heisenberg Hamiltonian for the magnetic hexagon with the single-node spin 1/2 and isotropic exchange interactions. It follows that eigenenergies and eigenstates are expressible within an extension of the prime field ℚ of rationals of degree 2^3 and 2^4, respectively. In quantum information setting, each real extension of rank 2 represents an arithmetic qubit. We demonstrate in detail some actions of the Galois group on the eigenproblem.
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