Supersolid phase of Three-dimensional spin and hardcore-boson models

TL;DR

This paper investigates the stability of solid and supersolid phases in three-dimensional spin and hardcore-Bose-Hubbard models, emphasizing quantum fluctuations' role and their impact on phase transitions near helium-4 parameters.

Contribution

It introduces a method to analyze quantum effects on supersolid stability using spinwave bosons and effective interactions, combining semiclassical and Ising expansions with ladder approximation.

Findings

Quantum fluctuations can destabilize the solid phase near helium-4 parameters.

Repulsive effective interactions are necessary for second-order solid-supersolid transitions.

Quantum effects depend critically on the energies of solid and superfluid phases at half filling.

Abstract

We study the stability of solid- and supersolid (SS) phases of a three-dimensional spin- and a hardcore-Bose-Hubbard models on a body-centered cubic lattice. To see the quantum effects on the stability of the SS phase, we model the vacancies (interstitials) introduced in the solid, which are believed responsible for the appearance of the SS phase, by spinwave bosons and adopt the interaction between the condensed bosons as a criterion. A repulsive nature of the low-energy effective interaction is the necessary condition for a second-order solid-SS transition and, when this condition is met, normally the SS phase is expected. In calculating the effective interaction, we use expansions from the semiclassical- (i.e. large-S) and the Ising limit combined with the ladder approximation. The impact of quantum fluctuations crucially depends on the energy of the solid phase and that of the superfluid phase at half filling. As an application to 4He, we study the parameter region in the vicinity of the fitting parameter set given by Liu and Fisher. For this parameters set, quantum fluctuations at the second order in 1/S destabilize the solid phase, which is supposed to be stable within the mean field theory.