Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring |
| G. Banaszaka, S. Barańczuk a, T. Lulek b, J. Milewski c and R. Stagraczyński d
aDepartment of Mathematical and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland bDepartment of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland cInstitute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland dChair of Physics, Rzeszów University of Technology, Powstańców Warszawy 6, 35-959 Rzeszów, Poland |
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| 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 23 and 24, 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. |
| DOI: 10.12693/APhysPolA.121.1111 PACS numbers: 03.65.Aa, 73.21.-b, 85.35.Be, 89.70.Eg |