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Journal of Physics Conference Series

Some results of exact solutions for the two-spin-flip number problem of the spin-1 Heisenberg chain

Yangdong Zheng

Published Jul 1, 2018• 0 citations
Publisher

Abstract

The eigenvalues and eigenvectors of the spin-1 Heisenberg chain are not exactly soluble by using of the Bethe Ansatz method. As an attempt, we propose a new format of the basic states and derive the exact solutions for the two-spin-flip number problem of the spin-1 Heisenberg chain. We discuss qualitatively some basic features of the above model for different types of wave number values.

DOI
10.1088/1742-6596/1053/1/012071

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The eigenvalues and eigenvectors of the spin-1 Heisenberg chain are not exactly soluble by using of the Bethe Ansatz method. As an attempt, we propose a new format of the basic states and derive the exact solutions for the two-spin-flip number problem of the spin-1 Heisenberg chain. We discuss qualitatively some basic features of the above model for different types of wave number values.
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We investigate symmetry properties of the Bethe ansatz wave functions for the Heisenberg XXZ spin chain. The XXZ Hamiltonian commutes simultaneously with the shift operator T and the lattice inversion operator V in the space of Ω=±1 with Ω the eigenvalue of T. We show that the Bethe ansatz solutions with normalizable wave functions cannot be the eigenstates of T and V with quantum number (Ω, ϒ)=(±1, ∓1) where ϒ is the eigenvalue of V. Therefore, the Bethe ansatz wave functions should be singular for nondegenerate eigenstates of the Hamiltonian with quantum number (Ω, ϒ)=(±1, ∓1). It is also shown that such states exist in any nontrivial down-spin number sector and that the number of them diverges exponentially with the chain length.
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