Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains

Abstract

The energy level density distributions of some Haldane-Shastry like spin chains associated with the $A_{N-1}$ root system have been computed recently by Enciso et al., exploiting the connection of these spin systems with inhomogeneous one-dimensional vertex models whose energy functions depend on the vertices through specific polynomials of first or second degree. Here we consider a much broader class of one-dimensional vertex models whose energy functions depend on the vertices through arbitrary polynomials of any possible degree. We estimate the order of mean and variance for such energy functions and show that the level density distribution of all vertex models belonging to this class asymptotically follow the Gaussian pattern for large number of vertices. We also present some numerical evidence in support of this analytical result.

22 pages, 2 figures, corrected minor typos, added one reference

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Cited by in corpus (6)

• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Yangian-invariant spin models and Fibonacci numbers
• Integrable open spin chains related to infinite matrix product states
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators