Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

Details Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

2006-04-13

arxiv.org/abs/math-ph/0604029v1

Commun. Math. Phys. 267 (2006), 451-476.

Physics

Mathematical Physics

25 pages, LaTeX

Scientific paper

10.1007/s00220-006-0076-3

We introduce an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials. The corresponding (finite-dimensional) spectral problem of the integrable lattice model is solved by means of the Bethe Ansatz method. The resulting eigenfunctions turn out to be given by specializations of the Hall-Littlewood polynomials. In the continuum limit the solution of the repulsive delta Bose gas due to Lieb and Liniger is recovered, including the orthogonality of the Bethe wave functions first proved by Dorlas (extending previous work of C.N. Yang and C.P. Yang).

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