2015/08/24 by Karol K. Kozłowski, Kozlowski, K. K.
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum many-body systems #Random Matrices and Applications #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1508.05741
openalex publication_date 2015/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathfrakm ∈ [0;1/2] exist and form, in the infinite volume limit, a dense distribution on a subinterval of ℝ. The results holds for any value of the anisotropy Δ≥ -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.