Jian-feng Wu, Ming Yu. Calogero-sutherland model in interacting fermion picture and explicit construction of Jack states
Submitted on: Jul 19, 2012, 02:45:27
Natural Sciences / Physics / Particle physics
Description: The 40-year-old Calogero-Sutherland (CS) model remains a source of inspirations for understanding 1d interacting fermions. At beta=1, or 0, the CS model describes a free non-relativistic fermion, or boson theory, while for generic beta, the system can be interpreted either as interacting fermions or bosons, or free anyons depending on the context. However, we shall show in this letter that the fermionic picture is advantageous in diagonalizing the CS Hamiltonian. Comparing to the previously known multi-integral representation or the Dunkl operator formalism for the CS wave functions, our method depends on the (upper or lower) triangular nature of the fermion interaction, which is resolved in perturbation theory of the second quantized form. The eigenstate is constructed from a multiplet of unperturbed states and the perturbation is of finite order. The full construction is a similarity transformation from the free fermion theory, in the same spirit as the Landau Fermi liquid theory and the 1d Luttinger liquid theory.
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