General energy bounds for systems of bosons with soft cores

TL;DR

This paper derives explicit bounds for the ground-state energy of bosonic systems with soft-core interactions, using variational methods and collective field theory, applicable in multiple dimensions.

Contribution

It introduces a systematic approach to bounding the energy of bosonic systems with specific pair potentials using variational and large-N techniques.

Findings

Explicit upper and lower bounds for ground-state energy derived

Bounds applicable in arbitrary dimensions greater than 2

Method can be improved via large-N collective field theory

Abstract

We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and lower bound formulas for the N-particle ground-state energy in arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is demonstrated that the upper bound can be systematically improved with the aid of a special large-N limit in collective field theory.