Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators

Abstract

We consider a $A_{N-1}$ type of spin dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as easily as its standard $su(M)$ invariant counterpart through the diagonalisation of Dunkl operators. A class of novel representations of the permutation operator $P_{ij}$, which pick up nontrivial phase factors along with interchanging the spins of $i$-th and $j$-th particles, are subsequently constructed. These `anyon like' representations interestingly lead to different variants of spin Calogero-Sutherland model with highly nonlocal interactions. We also explicitly derive some exact eigenfunctions as well as energy eigenvalues of these models and observe that the related degeneracy factors crucially depend on the choice of a few discrete parameters which characterise such anyon like representations.

25 pages, plain LaTex file, the results of sec.4 are presented in a more explicit way, to appear in Nucl. Phys.B

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• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
• Algebraic approach in unifying quantum integrable models
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• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
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• Solvable scalar and spin models with near-neighbors interactions
• Multi-parameter deformed and nonstandard $Y(g{l}_M)$ Yangian symmetry in a novel class of spin Calogero-Sutherland models
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Multiparametric and coloured extensions of the quantum group $G{L}_q(N)$ and the Yangian algebra $Y(g{l}_N)$ through a symmetry transformation of the Yang-Baxter equation
• Cosine series quantum sampling method with applications in signal and image processing
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• A Haldane-Shastry spin chain of BC_N type in a constant magnetic field
• Multi-parameter deformed and nonstandard $Y(g{l}_M)$ Yangian symmetry in integrable variants of Haldane-Shastry spin chain