An exactly solvable many-body problem in one dimension and the short-range Dyson model

Abstract

For N impenetrable particles in one dimension with upto next-to-nearest neighbours interaction, we obtain the exact ground state. We establish a mapping between these N-body problems and the short-range Dyson model introduced recently to model intermediate spectral statistics. We prove the absence of long-range order and off-diagonal long-range order in the corresponding many-body theory.