Path integral Monte Carlo is a computational method commonly used in statistical mechanics to numerically evaluate integrals in quantum mechanics. It is based on the Feynman path integral formulation, and uses Monte Carlo sampling techniques to approximate the path integral over all possible paths of a quantum system.
Unlike other Monte Carlo methods that sample from a single configuration of a system, PIMC samples from all possible paths of a system. This allows for the study of quantum systems at finite temperatures, where the system can exist in multiple configurations simultaneously.
The main steps in PIMC involve discretizing the imaginary time path integral into a finite number of slices, constructing a path integral representing the partition function, and then using Monte Carlo sampling to evaluate the path integral. This is done by randomly generating paths of the system and accepting or rejecting them based on their weight in the path integral.
PIMC has a wide range of applications in various fields such as condensed matter physics, nuclear physics, and quantum chemistry. It is commonly used to study the properties of quantum systems at finite temperatures, including the calculation of thermodynamic quantities, phase transitions, and spectral properties.
There are various books and online resources available for learning and implementing PIMC, including "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets" by Hagen Kleinert, and "Quantum Monte Carlo: Origins, Development, Applications" by James B. Anderson. Additionally, many software packages such as PIMC++ and PIMCpack are available for implementing PIMC simulations.