Bose-Einstein Quantum Statistics and the Ground State of Solid 4He

TL;DR

This study uses diffusion Monte Carlo with a new symmetric trial wave function to investigate the ground state and supersolid properties of solid helium-4, revealing tiny condensate fractions and superfluid densities, especially with vacancies.

Contribution

Introduces a novel symmetric trial wave function for solid helium-4 that accurately reproduces the equation of state and enables detailed supersolid property analysis.

Findings

Existence of off-diagonal long-range order with a condensate fraction ~10^{-4}

Superfluid density below 10^{-5} in a perfect crystal

Superfluid density increases to ~3.2×10^{-3} with 1% vacancies

Abstract

The ground state of solid $^4$He is studied using the diffusion Monte Carlo method and a new trial wave function able to describe the supersolid. The new wave function is symmetric under the exchange of particles and reproduces the experimental equation of state. Results for the one-body density matrix show the existence of off-diagonal long-range order with a very small condensate fraction $\sim 10^{-4}$. The superfluid density of the commensurate system is below our resolution threshold, $\rho_s/\rho < 10^{-5}$. With a 1% concentration of vacancies the superfluid density is manifestly larger, $\rho_s/\rho=3.2(1) \cdot 10^{-3}$.