Off-diagonal long-range order in one-dimensional many-body problem

TL;DR

This paper proves the existence of off-diagonal long-range order in a one-dimensional many-body quantum system, demonstrating the possibility of Bose-Einstein condensation in 1D, which is rare in statistical mechanics.

Contribution

It provides the first example of quantum phases and Bose-Einstein condensation in a one-dimensional statistical mechanics model.

Findings

Off-diagonal long-range order is established in the model.

The model relates to systems with intermediate statistics like the Anderson transition.

It suggests the possibility of Bose-Einstein condensation in 1D systems.

Abstract

We prove that there is off-diagonal long-range order in the symmetrised version of the one-dimensional many-body problem presented by Jain and Khare (Phys. Lett. A262 (1999)35). This model is related to the short-range Dyson model employed to study intermediate statistics in systems like the Anderson model in three dimensions at the metal-insulator transition point and pseudointegrable billiards. To the best of our knowledge, this is the only example showing quantum phases and possibility of Bose-Einstein condensation in one-dimensional statistical mechanics.