Isolated eigenvalues of the ferromagnetic spin-JXXZ chain with kink boundary conditions

Jaideep Mulherkar, Bruno Nachtergaele, Robert J Sims, Shannon Starr

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3 Scopus citations

Abstract

We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.

Original languageEnglish (US)
Article numberP01016
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2008
Issue number1
DOIs
Publication statusPublished - 2008
Externally publishedYes

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Keywords

  • Ladders and planes (theory)
  • Rigorous results in statistical mechanics
  • Spin chains

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistical and Nonlinear Physics

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