Path-integral simulation of solids

TL;DR

This paper reviews path-integral quantum simulation techniques for solids, covering methods, applications to various materials, and phenomena like phase transitions and quantum effects, especially in hydrogen-containing solids.

Contribution

It introduces practical path-integral simulation methods for solids and reviews their applications to diverse materials and phenomena, emphasizing nuclear quantum effects in light atoms.

Findings

Effective simulation of noble-gas solids and semiconductors.

Observation of quantum effects in hydrogen and ice.

Analysis of phase transitions and anharmonic effects.

Abstract

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques 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.