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Nuclear Physics B

Spin chains viewed as the fermionic parts of supersymmetric quantum mechanical models

Alan Macfarlane

Published Apr 1, 1995• 8 citations
Publisher
DOI
10.1016/0550-3213(94)00576-z

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Australian Journal of Physics•Jun 1, 1991•0 citations
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 types of supersymmetric PF spin chains, where K ⩽ 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 neighbor spacing distribution, are also studied.
An algebraic view of supersymmetric quantum mechanics is taken, emphasising the couplings between bosonic and fermionic modes in the supercharges. A class of model Hamiltonians is introduced wherein the fermionic (bosonic) operators are canonical and the bosonic (fermionic) ones satisfy a Lie algebra (superalgebra) whose representation theory permits the complete solution of the model in principle. The kinematical symmetry of such models is also described. The examples of one and two bosonic models, with 5U(2) and 5U(3) dynamical algebras respectively, are analysed in detail.