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arXiv · 1511.05909

Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators

P. Banerjee·B. Basu-Mallick·N. Bondyopadhaya·C. Datta
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Abstract

We derive the exact spectra as well as partition functions for a class of $BC_N$ type of spin Calogero models, whose Hamiltonians are constructed by using supersymmetric analogues of polarized spin reversal operators (SAPSRO). The strong coupling limit of these spin Calogero models yields $BC_N$ type of Polychronakos-Frahm (PF) spin chains with SAPSRO. By applying the freezing trick, we obtain an exact expression for the partition functions of such PF spin chains. We also derive a formula which expresses the partition function of any $BC_N$ type of PF spin chain with SAPSRO in terms of partition functions of several $A_K$ type of supersymmetric PF spin chains, where $K\leq N-1$. Subsequently we show that an extended boson-fermion duality relation is obeyed by the partition functions of the $BC_N$ type of PF chains with SAPSRO. Some spectral properties of these spin chains, like level density distribution and nearest neighbour spacing distribution, are also studied.

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P. Banerjee, B. Basu-Mallick, N. Bondyopadhaya, C. Datta. 2015-11-18. Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators. https://doi.org/10.1016/j.nuclphysb.2016.01.015

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