Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

• Authors: G. Banaszak , S. Barańczuk , T. Lulek , J. Milewski , R. Stagraczyński
• Languages of publication: EN

Abstracts

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.

Keywords

EN

03.65.Aa; 73.21.-b; 85.35.Be; 89.70.Eg

Discipline

• 89.70.Eg: Computational complexity
• 03.65.Aa: Quantum systems with finite Hilbert space
• 73.21.-b: Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems(for electron states in nanoscale materials, see 73.22.-f)
• 85.35.Be: Quantum well devices (quantum dots, quantum wires, etc.)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 5-6
• Pages: 1111-1114

Dates

published

2012-05

Contributors

author

G. Banaszak

• Department of Mathematical and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

author

S. Barańczuk

• Department of Mathematical and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

author

T. Lulek

• Department of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

author

J. Milewski

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

author

R. Stagraczyński

• Chair of Physics, Rzeszów University of Technology, Powstańców Warszawy 6, 35-959 Rzeszów, Poland

References

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Identifiers

DOI

10.12693/APhysPolA.121.1111