Energy of N two-dimensional bosons with zero-range interactions

TL;DR

This paper derives an integral equation for N two-dimensional bosons with zero-range interactions, solves it numerically for up to 26 particles, and confirms the large-N energy scaling predicted by previous theoretical work.

Contribution

It introduces a new integral equation for the system and applies stochastic Monte Carlo methods to compute ground state energies for larger N than previously possible.

Findings

Confirmed the large-N energy scaling law.

Extended numerical calculations up to 26 particles.

Validated the theoretical predictions with numerical evidence.

Abstract

We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling $B_N\propto 8.567^N$ predicted by Hammer and Son [Phys. Rev. Lett. {\bf 93}, 250408 (2004)] in the large-$N$ limit.