An exactly solvable many-body problem in one dimension

TL;DR

This paper presents an exactly solvable one-dimensional many-body problem with specific interactions, providing complete spectral solutions, a mapping to a Dyson model, and insights into correlation functions and long-range order.

Contribution

It introduces a novel exactly solvable model for N impenetrable particles with nearest and next-to-nearest interactions and connects it to the Dyson model for spectral statistics.

Findings

Complete spectrum obtained for the model

Mapping established with the short-range Dyson model

Proven absence of long-range and off-diagonal long-range order

Abstract

For N impenetrable particles in one dimension where only the nearest and next-to-nearest neighbours interact, we obtain the complete spectrum both on a line and on a circle. Further, we establish a mapping between these N-body problems and the short-range Dyson model introduced recently to model intermediate spectral statistics in some systems using which we compute the two-point correlation function and prove the absence of long-range order in the corresponding many-body theory. Further, we also show the absence of off-diagonal long-range order in these systems.