Path integral calculations of vacancies in solid Helium
We study properties of vacancies in solid 4He using Path Integral Monte Carlo. We find, in agreement with other calculations, that the energy to create a single vacancy is 11.5 K and is monotonic with the number of vacancies. If more then a few percent of the system becomes vacant, we find the system becomes unstable to melting. We show the number of exchanges in the system is increased by vacancies and how the underlying lattice is altered by the presence of a vacancy. We also examine the efficacy of using a tight binding Hamiltonian to describe the vacancy in the crystal, show that vacancies are attractive, and find values for the effective mass and inter-vacancy attraction.
Path-integral simulation of solids
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron–phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.
Superfluidity or supersolidity as a consequence of off-diagonal long-range order
We present a general derivation of Hess-Fairbank effect or nonclassical rotational inertial (NCRI), i.e., the refusal to rotate with its container, as well as the quantization of angular momentum, as consequences of off-diagonal long-range order (ODLRO) in an interacting Bose system. Afterwards, the path integral formulation of superfluid density is rederived without ignoring the centrifugal potential. Finally and in particular, for a class of variational wave functions used for solid helium, treating the constraint of single-valuedness boundary condition carefully, we show that there is no ODLRO and, especially, demonstrate explicitly that NCRI cannot be possessed in absence of defects, even though there exist zero-point motion and exchange effect.