Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 091, 13 pages      arXiv:1008.5285      https://doi.org/10.3842/SIGMA.2010.091

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

Bireswar Basu-Mallick a, Nilanjan Bondyopadhaya b and Kazuhiro Hikami c
a) 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, Santiniketan 731 235, India
c) Department of Mathematics, Naruto University of Education, Tokushima 772-8502, Japan

Received September 06, 2010, in final form November 30, 2010; Published online December 10, 2010

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.

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

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