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arXiv · 1508.05741

On condensation properties of Bethe roots associated with the XXZ chain

K. K. Kozlowski
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Abstract

I prove that the Bethe roots describing either the ground state or a certain class of "particle-hole" excited states of the XXZ spin-$1/2$ chain in any sector with magnetisation $\mathfrak{m} \in [0;1/2]$ exist and form, in the infinite volume limit, a dense distribution on a subinterval of $\mathbb{R}$. The results holds for any value of the anisotropy $Δ\geq -1 $. In fact, I establish an even stronger result, namely the existence of an all order asymptotic expansion of the counting function associated with such roots. As a corollary, these results allow one to prove the existence and form of the infinite volume limit of various observables attached to the model -the excitation energy, momentum, the zero temperature correlation functions, so as to name a few- that were argued earlier in the literature.

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K. K. Kozlowski. 2017-09-14. On condensation properties of Bethe roots associated with the XXZ chain. https://arxiv.org/abs/1508.05741

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