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

TL;DR

This paper derives exact spectra and partition functions for supersymmetric $BC_N$ type spin Calogero models with polarized spin reversal operators, revealing their spectral properties and dualities.

Contribution

It introduces a new class of supersymmetric $BC_N$ type models with polarized spin reversal operators and provides explicit formulas for their spectra and partition functions.

Findings

Exact spectra and partition functions derived.

Partition functions expressed in terms of $A_K$ type chains.

Spectral properties like level density and spacing analyzed.

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.