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Path Integral Monte Carlo

By John Shumway1, Matthew Gilbert2

1. Arizona State University 2. University of Texas at Austin

Path Integral Monte Carlo

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Archive Version 1.2.1
Published on 27 Mar 2008, unpublished on 23 Jul 2008
Latest version: 1.2.2. All versions

doi:10.4231/D3GT5FF39 cite this

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Abstract

Path integral Monte Carlo (PIMC) simulates particles (often electrons and ions) by directly sampling the canonical partition function. In the path integral formulation of quantum statistical mechanics developed by Richard Feynman, particles get represented by closed imaginary-time trajectories of length h/kT. PIMC simulations are able to compute total energies, correlation functions, charge distribution, and linear response functions for thermal equilibrium. As in many quantum Monte Carlo methods, PIMC has efficient scaling with system size, often order N or N2.

Our application, pi or app-pimc, is well suited for modeling conduction electrons in quantum dots, quantum wires, and quantum wells. We have also tested it for ab initio calculations, but at this point only hydrogen and helium atoms work well. The app-pimc tool is a low-level wrapper for our application that allows the user to input a simulation description in XML, run the simulation in 1, 2, or 3 dimensions, and view results of scalar estimators. While this is an expert interface, we provide demo input files for quick simulations of a free particle, simple harmonic oscillator, and a hydrogen atom. The code is open source, so users have the option of installing a local version of the program on their machines if that better suites their research.

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