Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores

TL;DR

This paper investigates the connection between long particle cycles and Bose-Einstein condensation in an infinite-range Bose-Hubbard model with hard-core interactions, revealing that long cycles coincide with condensation but do not match condensate density.

Contribution

It provides a detailed analysis of long cycle densities in the model and clarifies their relationship with Bose-Einstein condensation, highlighting differences in their densities.

Findings

Long cycle density coincides with Bose-Einstein condensation occurrence.

Long cycle density is not equal to the condensate density.

Bose-Einstein condensation is characterized by the presence of long cycles.

Abstract

In this paper we study the relation between long cycles and Bose-Condensation in the Infinite range Bose-Hubbard Model with a hard core interaction. We calculate the density of particles on long cycles in the thermodynamic limit and find that the existence of a non-zero long cycle density coincides with the occurrence of Bose-Einstein condensation but this density is not equal to that of the Bose condensate.