# On condensation properties of Bethe roots associated with the XXZ chain

Source: [On condensation properties of Bethe roots associated with the XXZ chain](<https://www.sota2.com/research/paper/68fa365f1e209131ce8a97d5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:47:47.439Z

Authors: K. K. Kozlowski

Published: 2015-08-24T10:08:00.000Z

## 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 $\\Delta \\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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1508.05741>)

[PDF](<https://arxiv.org/pdf/1508.05741.pdf>)