Exact spectrum and partition function of \(SU(m|n)\) supersymmetric Polychronakos model. (English) Zbl 0977.82008
By using the fact that Polychronakos-like models can be obtained through the ‘freezing limit’ of related spin Calogero models, we calculate the exact spectrum as well as the partition function of the \(SU(m|n)\) supersymmetric Polychronakos (SP) model. It turns out that, similar to the non-supersymmetric case, the spectrum of the \(SU(m|n)\) SP model is also equally spaced. However, the degeneracy factors of corresponding energy levels crucially depend on the values of bosonic degrees of freedom \((m)\) and fermionic degrees of freedom \((n)\). As a result, the partition functions of the SP models are expressed with some novel \(q\)-polynomials. Finally, by interchanging the bosonic and fermionic degrees of freedom, we obtain a duality relation among the partition functions of the SP models.
MSC:
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
81T60 | Supersymmetric field theories in quantum mechanics |
33D90 | Applications of basic hypergeometric functions |
81V70 | Many-body theory; quantum Hall effect |