1998/04/20 by Rahul Siddharthan, Siddharthan, Rahul
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Quantum and electron transport phenomena #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.cond-mat/9804210
12 pages, latex, no figures
arxiv created 1998/04/20 · openalex publication_date 1998/04/20 · arxiv updated 2009/11/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We examine the question of whether Bethe's ansatz reproduces all states in\nthe periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself,\nthere are states for which the Bethe momenta kn diverge: these are in fact\nthe simplest examples of ``string'' solutions. The coefficients of the Bethe\nwavefunction, too, diverge. When there are only two down spins in the system\n(the case considered by Bethe), we can renormalize these coefficients to get a\nsensible (and correct) wavefunction. We show that this is not always possible\nwhen there are more than two down spins. The Bethe equations have several such\ndivergent solutions, and some of these correspond to genuine eigenfunctions of\nthe Hamiltonian, but several do not. Nor do they reproduce the correct energy\neigenvalues. Moreover, we point out that the algebraic Bethe ansatz, an\nalternative way to construct the wavefunctions proposed by Faddeev, Takhtajan\net al., leads to vanishing wavefunctions for all these solutions. Thus, the\nBethe ansatz solution of the Heisenberg model must be regarded as either\nincomplete, or inaccurate.\n