2020/10/16 by Jose Carrasco, Carrasco, Jose, Federico Finkel +5
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.2010.08307
51 pages, typeset with LaTeX
arxiv created 2020/10/16 · arxiv updated 2020/10/19
We study the open version of the su(m|n) supersymmetric Haldane-Shastry spin chain associated to the BCN 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 BCN 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.