2019•arXiv (Cornell University)Open access

Markov Chain Monte Carlo Methods in Quantum Field Theories: A Modern Primer

Anosh Joseph

Abstract

We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian Monte Carlo, are introduced. We review the underlying theoretical foundations of Markov chain Monte Carlo. We provide several examples of Monte Carlo simulations, including one-dimensional simple harmonic oscillator, unitary matrix model exhibiting Gross-Witten-Wadia transition and a supersymmetric model exhibiting dynamical supersymmetry breaking.

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Key concepts: Quantum Monte Carlo, Hybrid Monte Carlo, Monte Carlo method in statistical physics, Monte Carlo method, Monte Carlo molecular modeling, Statistical physics, Markov chain Monte Carlo, Dynamic Monte Carlo method