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

We derive the exact spectra as well as partition functions for a class of BCNBCN 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 BCNBCN 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 BCNBCN type of PF spin chain with SAPSRO in terms of partition functions of several AKAK types of supersymmetric PF spin chains, where K⩽N−1K⩽N−1. Subsequently we show that an extended boson–fermion duality relation is obeyed by the partition functions of the BCNBCN type of PF chains with SAPSRO. Some spectral properties of these spin chains, like level density distribution and nearest neighbor spacing distribution, are also studied.