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arXiv · 2010.08307

The open supersymmetric Haldane-Shastry spin chain and its associated motifs

Jose Carrasco·Federico Finkel·Artemio González-López·Miguel A. Rodríguez
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Abstract

We study the open version of the su$(m|n)$ supersymmetric Haldane-Shastry spin chain associated to the $BC_N$ extended root system. We first evaluate the model's partition function by modding out the dynamical degrees of freedom of the su$(m|n)$ supersymmetric spin Sutherland model of $BC_N$ 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$(1|1)$ model finding an analytic expression for its Helmholtz free energy in the thermodynamic limit.

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Jose Carrasco, Federico Finkel, Artemio González-López, Miguel A. Rodríguez. 2020-10-16. The open supersymmetric Haldane-Shastry spin chain and its associated motifs. https://arxiv.org/abs/2010.08307

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