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

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 E₁/E₀∼ |D-2|^-α|lnγ| ^-α′ where D is the spatial dimension, and γ is the gas parameter (γ = na^D). As D →2, α = α′ = 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 than unity.