Wave functions for gas/liquid phases when the ground state is crystalline

Determine which many-body wave functions can adequately describe the gaseous or liquid phase of a Bose system whose ground state is crystalline, in a way that avoids the non‑isotropic dispersion that arises from using excited-state constructions built on an anisotropic crystalline ground-state wave function.

Background

The paper presents exact wave-function expansions for ground and excited states of interacting bosons in terms of Bose-symmetric basis functions. For gaseous or liquid phases, formulas (9)–(12) are preferred, while equation (21) provides an alternative representation.

However, the authors note a conceptual gap when the system’s ground state is crystalline: constructing excited states on a crystalline ground-state wave function leads to non-isotropic dispersion, which is unsuitable for describing isotropic gaseous or liquid phases. They remark that they have not found a prior resolution to this issue in the literature and suggest that the alternative representation (21) may be suitable, leaving open the broader question of what wave-function forms are appropriate in this setting.