Explorations of the Microstructure of Crystalline Quantum Many-Body Systems

Abstract

We undertake a formal analysis of crystallographic point and space group symmetries in the one-body density and in the two-body density of strongly correlated many-body systems. The mathematical tools presented in this article are put to a numerical test in an exact Fourier path integral Monte Carlo simulation of solid natural argon at the triple point temperature in the hexagonal close-packed structure. We point out the experimental significance of this system in particular and, more generally, briefly describe how quantities computed within the approach taken in the present work may be directly related to experimentally measurable quantities. We also address the potential relevance of the techniques presented and tested in this paper to the liquid-to-solid phase transition. The group-theoretical formalism developed in this work is of general validity and might be a valuable means also for other condensed matter theories, e.g., for applications of correlated basis functions and correlated density matrix theories of the ground state and of the collective excitations of quantum many-body systems to quantum crystals.