Bounds on the mass gap of the ferromagnetic XXZ chain

1995/01/20 by Bruno Nachtergaele, Nachtergaele, Bruno · 1 citation
Mathematics · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Quantum many-body systems #Random Matrices and Applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.cond-mat/9501098

openalex publication_date 1995/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove rigorous lower and upper bounds for the mass gap of the ferromagnetic spin 1/2 XXZ chain. The two bounds coincide asymptotically in the Ising limit Δ→∞. Near the isotropic point, Δ=1, the estimates are good enough to determine the critical behaviour of the mass gap unambiguously. The derivation does not rely on exact solutions.

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• Low Temperature Results for the Heisenberg XXZ and XY Models

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