skip to main content

Title: A new perspective on the integrability of Inozemtsev’s elliptic spin chain

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane–Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev’s chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane–Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane–Shastry chain. - Highlights: • Construction of Inozemtsev’s elliptic spin chain using Polychronakos’s freezing trick. • Numerical evidence of the Gaussianmore » character of the level density. • Exact computation and asymptotics of the mean and standard deviation of the spectrum. • Evidence of the chain’s integrability from key statistical properties of its spectrum. • Exact evaluation of finite sums of powers of Weierstrass’s elliptic function.« less
Authors:
;
Publication Date:
OSTI Identifier:
22403500
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; CALCULATION METHODS; ENERGY-LEVEL DENSITY; FLUCTUATIONS; INTEGRAL CALCULUS; INTERACTION RANGE; QUANTUM SYSTEMS; SPECTRA; SPECTRA UNFOLDING; SPIN