AN EXACTLY SOLVABLE MANY-BODY PROBLEM IN ONE DIMENSION

Abstract

We obtain the exact ground state of N-particles in one dimension both on a line and on a circle in case the N particles are interacting via nearest and next-to-nearest neighbour interactions. Further, we establish a mapping between these N-body problems and short range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute one and two point functions of a related many-body theory in the thermodynamic limit and show the absence of long range order. Generalization of the model on the line to higher dimensions as well as to other root systems is also considered. Finally, we also consider a variant of the above model in two dimensions in which all the states exhibit novel correlations.