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Heisenberg and Bethe Field Extensions Applied to Magnetic Rings

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Banaszak G., Blinkiewicz D., Krasoń P., Milewski J.

Acta Physica Polonica A

2018

vol. 133

issue 3

441-443

We consider striking connections between the theory of homogenous isotropic Heisenberg ring (XXX-model) and algebraic number theory. We explain the nature of these connections especially applications of Galois theory for computation of the spectrum of the Heisenberg operators and Bethe parameters. The solutions of the Heisenberg eigenproblem and Bethe Ansatz generate interesting families of algebraic number fields. Galois theory yields additional symmetries which not only simplify the analysis of the model but may lead to new applications and horizons.

Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

88%

Banaszak G., Barańczuk S., Lulek T., Milewski J., Stagraczyński R.

Acta Physica Polonica A

2012

vol. 121

issue 5-6

1111-1114

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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2 Acta Physica Polonica A

1 2018

1 2012

2 Banaszak G.

2 Milewski J.

1 Barańczuk S.

1 Blinkiewicz D.

1 Krasoń P.

1 Lulek T.

1 Stagraczyński R.

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Heisenberg and Bethe Field Extensions Applied to Magnetic Rings

Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring