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Physical review. B, Condensed matter

Exact solution of a two-component Calogero-Sutherland model with molecular field

Junpeng Cao, Gang Xiong, Rui‐Hong Yue, Yupeng Wang

Published Jun 20, 2002• 1 citation
Publisher

Abstract

By constructing the spin-Dunkl operators, a two-component Calogero-Sutherland model with molecular field is established. The integrability of the system is proved by constructing the conserved quantities. With the use of the asymptotic Bethe ansatz method, the exact solution of the model is derived and the thermodynamics of the rational limit is discussed.

DOI
10.1103/physrevb.66.014403

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By constructing the spin-Dunkl operators, a two-component Calogero-Sutherland model with molecular field is established. The integrability of the system is proved by constructing the conserved quantities. With the use of the asymptotic Bethe ansatz method, the exact solution of the model is derived and the thermodynamics of the rational limit is discussed.
Explicit-exact expressions for the particle propagator of the spin 1/2 Calogero–Sutherland model are derived for the system of a finite number of particles and for that in the thermodynamic limit. Derivation of the expression in the thermodynamic limit is also presented in detail. Combining this result with the hole propagator obtained in earlier studies, we calculate the spectral function of the single particle Green's function in the full range of the energy and momentum space. The resultant spectral function exhibits power-law singularity characteristic to correlated particle systems in one dimension.
We study the trigonometric quantum spin-Calogero-Sutherland model, and the Haldane-Shastry spin chain as a special case, using a Bethe-ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability for Heisenberg spin chains into the world of integrable long-range models with spins. From the transfer matrix with a diagonal twist we construct Heisenberg-style symmetries (Bethe algebra) that refine the usual hierarchy of commuting Hamiltonians (quantum determinant) of the spin-Calogero-Sutherland model. We compute the first few of these new conserved charges explicitly, and diagonalise them by Bethe ansatz inside each irreducible Yangian representation. This yields a new eigenbasis for the spin-Calogero-Sutherland model that generalises the Yangian Gelfand-Tsetlin basis of Takemura-Uglov. The Bethe-ansatz analysis involves non-generic values of the inhomogeneities. Our review of the inhomogeneous Heisenberg XXX chain, with special attention to how the Bethe ansatz works in the presence of fusion, may be of independent interest.