This article is cited in 19 papers

One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane–Shastry Like Spin Chains

Bireswar Basu-Mallick^a, Nilanjan Bondyopadhaya^b, Kazuhiro Hikami<sup>c

a</sup> Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700 064, India
^b Integrated Science Education and Research Centre, Siksha-Bhavana, Visva-Bharati
^c Department of Mathematics, Naruto University of Education, Tokushima 772-8502, Japan

Abstract: We define a class of $Y(sl_{(m|n)})$ Yangian invariant Haldane–Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with one-dimensional vertex models.

Keywords: Haldane–Shastry spin chain; vertex model; Yangian quantum group; boson-fermion duality relation.

MSC: 81R12; 81R50; 82B10; 82B05

Received: September 6, 2010; in final form November 30, 2010; Published online December 10, 2010

Language: English

DOI: 10.3842/SIGMA.2010.091

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ArXiv: 1008.5285