Supersymmetric analogue of \(\mathrm{BC}_{N}\) type rational integrable models with polarized spin reversal operators. (English) Zbl 1332.82063
Summary: We derive the exact spectra as well as partition functions for a class of \(\mathrm{BC}_N\) 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 \(\mathrm{BC}_N\) 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 \(\mathit{BC}_N\) type of PF spin chain with SAPSRO in terms of partition functions of several \(A_K\) types of supersymmetric PF spin chains, where \(K \leqslant N - 1\). Subsequently we show that an extended boson-fermion duality relation is obeyed by the partition functions of the \(\mathrm{BC}_N\) 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.
MSC:
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
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