Analytical and combinatorial aspects of the eigenproblem for the two-magnon sector of XXX Heisenberg rings

DOI10.1016/S0034-4877(20)30059-8zbMath1453.82011OpenAlexW3081787238MaRDI QIDQ2210548

Piotr Krasoń, Jan Milewski, M. Łabuz

Publication date: 7 November 2020

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(20)30059-8

zbMATH Keywords

Chebyshev polynomialBethe parametersHeisenberg ring

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Exactly solvable models; Bethe ansatz (82B23) Spinor and twistor methods applied to problems in quantum theory (81R25) Many-body theory; quantum Hall effect (81V70) Statistical mechanics of solids (82D20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical mechanics of magnetic materials (82D40) Fermionic systems in quantum theory (81V74)

Related Items (1)

Separation of spherically and translationally covariant finite quantum spaces within the XXX model

Cites Work

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• Where are the roots of the Bethe Ansatz equations?
• Direct diagonalisation of the Heisenberg Hamiltonian for a magnetic ring within the two-deviation sector by means of the Chebyshev polynomials
• Algebraic Bethe ansatz for singular solutions
• Exact quantum numbers of collapsed and non-collapsed two-string solutions in the spin-1/2 Heisenberg spin chain
• From asymptotic to finite Heisenberg chain—the evolution of Bethe solutions
• Continuity of Bethe solutions with respect to chain length N and winding numbers {λl}
• Singular solutions to the Bethe ansatz equations and rigged configurations

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