2015
DOI: 10.1088/1751-8113/48/17/175207
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Singular eigenstates in the even(odd) length Heisenberg spin chain

Abstract: We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions {λα} are invariant under the sign changes of their rapidities {λα} = {−λα}, then the Bethe ansatz equations are reduced to a system of (… Show more

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Cited by 6 publications
(8 citation statements)
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“…Distinct from studies of other integrable systems, the method presented does not assume knowledge of the distribution of Bethe roots, such as in a string hypothesis, nor is it reliant on counting the number of solutions. It is instead founded on the operator identities (7). This is an approach that can be generalised.…”
Section: Resultsmentioning
confidence: 99%
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“…Distinct from studies of other integrable systems, the method presented does not assume knowledge of the distribution of Bethe roots, such as in a string hypothesis, nor is it reliant on counting the number of solutions. It is instead founded on the operator identities (7). This is an approach that can be generalised.…”
Section: Resultsmentioning
confidence: 99%
“…provides a basis of eigenstates. For the XXX chain this is a problem which has attracted significant attention (see [2] for a historical overview), and one which has continued to produce research results up until recent times [3][4][5][6][7]. Similar analyses have been performed for other models, e.g.…”
Section: Introductionmentioning
confidence: 89%
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“…(28); a state like this is called a singular solution of the Bethe ansatz 90,91 . In fact, the state in Eq.…”
Section: A Two-particle Bound Statesmentioning
confidence: 99%
“…The Bethe ansatz equations for the spin-1/2 XXX and XXZ chains may have solutions containing a pair of pure imaginary rapidities (iζ/2, −iζ/2). We call them singular solutions [13,[18][19][20][21][22][23][24][25][26][27][28]. They make some factors of eqs.…”
Section: Introductionmentioning
confidence: 99%