Finite-size scaling behavior of Bose-Einstein condensation in the 1D Bose gas

TL;DR

This paper demonstrates the finite-size scaling behavior of Bose-Einstein condensation in a 1D Bose gas with repulsive interactions at zero temperature, revealing conditions under which condensate fraction remains finite as system size grows.

Contribution

The study provides an exact numerical analysis of BEC in 1D bosons, establishing a finite-size scaling law for the condensate fraction based on interaction strength and particle number.

Findings

Condensate fraction remains nonzero for large system sizes under specific scaling conditions.

Finite-size scaling function relates interaction parameter and particle number.

Condensate fraction is constant in thermodynamic limits for certain interaction scalings.

Abstract

Through exact numerical solutions we show Bose-Einstein condensation (BEC) for the one-dimensional (1D) bosons with repulsive short-range interactions at zero temperature by taking a particular large size limit. Following the Penrose-Onsager criterion of BEC, we define condensate fraction by the fraction of the largest eigenvalue of the one-particle reduced density matrix. % We show the finite-size scaling behavior such that condensate fraction is given by a scaling function of one-variable: interaction parameter multiplied by a power of particle number. Condensate fraction is nonzero and constant for any large value of particle number or system size, if the interaction parameter is proportional to the negative power of particle number. %Here the interaction parameter is defined by the coupling constant of the delta-function potentials devided by the density. %With the scaling behavior we derive various themodynamic limits where condensate fraction is constant for any large system size; for instance, it is the case even in the system of a finite particle number.