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This article is cited in 19 scientific papers (total in 19 papers)
One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane–Shastry Like Spin Chains
Bireswar Basu-Mallicka, Nilanjan Bondyopadhayab, Kazuhiro Hikamic 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
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.
Received: September 6, 2010; in final form November 30, 2010; Published online December 10, 2010
Citation:
Bireswar Basu-Mallick, Nilanjan Bondyopadhaya, Kazuhiro Hikami, “One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane–Shastry Like Spin Chains”, SIGMA, 6 (2010), 091, 13 pp.
Linking options:
https://www.mathnet.ru/eng/sigma549 https://www.mathnet.ru/eng/sigma/v6/p91
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