A class of N-body problems with nearest- and next-to-nearest neighbour interactions

Details A class of N-body problems with nearest- and next-to-nearest neighbour interactions A class of N-body problems with nearest- and next-to-nearest neighbour interactions

2000-04-03

arxiv.org/abs/cond-mat/0004012v1

J. Phys. A34 (2001) 695-724

Physics

Condensed Matter

LaTeX2e, 40 pages, 2 figures, submitted to Nucl. Phys. B [FS]

Scientific paper

10.1088/0305-4470/34/4/302

We obtain the exact ground state and a part of the excitation spectrum in one dimension on a line and the exact ground state on a circle in a case where N particles are interacting via nearest- and next-to-nearest neighbour interactions. Further, using the exact ground-state, we establish a mapping between these N-body problems and the short-range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute the one- and two-point functions of a related many-body theory and show that there is no long-range order in the thermodynamic limit. However, quite remarkably, we prove the existence of an off-diagonal long-range order in the symmetrised version of the related many-body theory. Generalisation of the models to other root systems is also considered. Besides, we also generalize the model on the full line to higher dimensions. Finally, we consider a model in two dimensions in which all the states exhibit novel correlations.

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