The open supersymmetric Haldane-Shastry spin chain and its associated motifs
Oct 16, 2020Citations per year
Abstract: (arXiv)
We study the open version of the su supersymmetric Haldane-Shastry spin chain associated to the extended root system. We first evaluate the model's partition function by modding out the dynamical degrees of freedom of the su supersymmetric spin Sutherland model of type, whose spectrum we fully determine. We then construct a generalized partition function depending polynomially on two sets of variables, which yields the standard one when evaluated at a suitable point. We show that this generalized partition function can be written in terms of two variants of the classical skew super Schur polynomials, which admit a combinatorial definition in terms of a new type of skew Young tableaux and border strips (or, equivalently, extended motifs). In this way we derive a remarkable description of the spectrum in terms of this new class of extended motifs, reminiscent of the analogous one for the closed Haldane-Shastry chain. We provide several concretes examples of this description, and in particular study in detail the su model finding an analytic expression for its Helmholtz free energy in the thermodynamic limit.Note:
- 51 pages, typeset with LaTeX
References(63)
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