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

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 $\cale_1/\cale_0 \sim |D-2|^{-\al}|\lnγ|^{-\al'}$, 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.

9 pages, 3 figures,