Quantum Monte Carlo Computation of Static and Time-Dependent Thermodynamic Properties of Lennard-Jones Crystals

Abstract

Recently there has been much interest in the study of the thermodynamics of many-body quantum mechanical systems by means of Quantum Monte Carlo (QMC) computer simulation techniques^(1–4). Applications of QMC methods to the study of spin systems, the Hubbard model, and to systems of boson and fermion particles have shown them to be effective in the accurate computation of static thermodynamic properties^(1–4). However, in spite of these successful QMC treatments of static thermodynamics, the determination of time-dependent thermodynamic averages (spin correlation functions, atomic displacement correlation functions, etc.), related to the time-dependent response of quantum many-body systems, has been less forthcoming. Aside from the increased bookkeeping difficulties associated with having to determine averages which depend on the new variable of time, one finds that this variable enters time-dependent computed averages in such a way that analytic continuation techniques, commonly employed in Green’s function treatments of such properties, are of little or no value in developing QMC methods for this problem.^(3,5)