First-order quantum correction to the ground-state energy density of two-dimensional hard-sphere Bose atoms

TL;DR

This paper derives the divergence behavior of the first-order quantum correction to the ground-state energy density of two-dimensional hard-sphere Bose atoms, revealing non-perturbative effects near two dimensions.

Contribution

It provides an effective field theory analysis of divergence exponents and characterizes the non-perturbative nature of quantum corrections in low-dimensional Bose gases.

Findings

Divergence exponents are obtained analytically.

Quantum correction becomes non-perturbative for dimensions below 2.2.

Correction scales as |D-2|^{-1} and | abla ext{ln}\gamma|^{-1} near D=2.

Abstract

Divergence exponents of the first-order quantum correction of a two-dimensional hard-sphere Bose atoms are obtained by an effective field theory method. The first-order correction to the ground-state energy density with respect to the zeroth-order is given by $\cale_1/\cale_0 \sim |D-2|^{-\al}|\ln\gamma|^{-\al'}$, where $D$ is the spatial dimension, and $\gamma$ is the gas parameter ($\gamma=n a^D$). As $D \to 2$, $\al =\al'=1$. We show that the first-order quantum correction of the energy density is not perturbative in low dimensions of $D < 2.2$ regardless of any gas parameter which is much less that 1.