Quantum Monte Carlo: From Few to Many Species

William G. Dawkins

Published May 1, 2019• 0 citations

Abstract

We study systems of particles with varying numbers of distinguishable species ranging from 4-species to the N-species limit, where N is the number of particles in the system itself. We examine these systems using various powerful simulation techniques that belong to the quantum Monte Carlo (QMC) family. The N-species limit is studied via Path Integral Monte Carlo (PIMC), which is a finite temperature, non-perturbative technique. At this limit, we explore the viability of two different thermal density matrices for systems that interact via hard-sphere, hard-cavity potentials. We then study the impact of finite-size effects on calculations of the energy, pressure and specific heat of the system when reaching the thermodynamic limit under periodic boundary conditions. We then move to studying a 4-species fermionic system using Variational Monte Carlo (VMC) and Diffusion Monte Carlo (DMC), which are ground state techniques. We apply these methods to the clustering problem of 4-particle and 8-particle systems. While the 4-particle, 4-species system is relatively simple to calculate as it is physically identical to a bosonic system of 4-particles, the 8-particle fermi system is more complicated. We detail the process of simulating a bound 8-particle state with respect to decay into two independent 4-particle clusters with DMC for the first time.

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