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

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• 作者：P. Banerjee^a ; ¹ ; ^{pratyaybanerjeesinp@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; B. Basu-Mallick^a ; ^{bireswar.basumallick@saha.ac.in" class="auth_mail" title="E-mail the corresponding author} ; N. Bondyopadhaya^b ; ² ; ^{nilanjan.iserc@visva-bharati.ac.in" class="auth_mail" title="E-mail the corresponding author} ; C. Datta^a ; ^{chitralekha.datta@saha.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Nuclear Physics B
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：904
• 期：Complete
• 页码：297-326
• 全文大小：540 K

文摘

We derive the exact spectra as well as partition functions for a class of BC_N${\mathit{BC}}_N$ 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${\mathit{BC}}_N$ 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${\mathit{BC}}_N$ type of PF spin chain with SAPSRO in terms of partition functions of several A_K$A_K$ types of supersymmetric PF spin chains, where K⩽N−1$K⩽N-1$. Subsequently we show that an extended boson–fermion duality relation is obeyed by the partition functions of the BC_N${\mathit{BC}}_N$ 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.