TL;DR
This paper reviews experimental facts and theories on supersolidity, proposing a Hartree-Fock approach for Boson solids, and introduces a novel state with superflow but lacking ODLRO, questioning its relevance to solid helium.
Contribution
It presents a Hartree-Fock description of Boson solids and introduces a new state of matter with superflow without ODLRO, based on the Boson Hubbard model.
Findings
Identification of a superflow state without ODLRO
Demonstration that local functions in Boson Hubbard model are non-orthogonal
Discussion on applicability to solid helium
Abstract
After reviewing some experimental facts, and early theories, I sketch the Hartree-Fock description of Boson solids, emphasizing the contrast with the Fermion case in that the natural solution is a product of local wave-functions. I then investigate the Boson Hubbard model to demonstrate that the local functions are not orthogonal and exemplify a novel state of matter which has superflow but not ODLRO, below a cooperative thermal transition. I then discuss whether or not these ideas actually apply to solid He.
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