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Institute of Physics eBooks

A Practical Course on Quantum Monte Carlo

V. Apaja

Published Aug 1, 2025• 0 citations
Publisher

Abstract

Covering topics including diffusion Monte Carlo, path integral Monte Carlo, variational Monte Carlo, and fermionic complexities (and many more), this book isn't merely a compendium of methods—it's a voyage of understanding. The book empowers readers to decipher the inner workings of Quantum Monte Carlo. It doesn't stop at equipping you with theories; it arms you with practical insights through sample codes, enabling you to deconstruct, analyze, and enhance existing algorithms. Ultimately, it showcases that Quantum Monte Carlo isn't just a numerical tool—it's an expedition that reveals the hidden facets of the quantum world. Part of IOP Series in Quantum Technology. Key features • Accompanying code and worked examples of how an algorithm can be coded and tested. • What makes Quantum Monte Carlo superior and just as importantly, what breaks it. • Teaches statistical physics and quantum physics in parallel. • Includes detailed mathematical derivations that won’t leave blind spots. • Emphasises Quantum Monte Carlo as a tool of visualizing quantum mechanics

DOI
10.1088/978-0-7503-6310-5

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Covering topics including diffusion Monte Carlo, path integral Monte Carlo, variational Monte Carlo, and fermionic complexities (and many more), this book isn't merely a compendium of methods—it's a voyage of understanding. The book empowers readers to decipher the inner workings of Quantum Monte Carlo. It doesn't stop at equipping you with theories; it arms you with practical insights through sample codes, enabling you to deconstruct, analyze, and enhance existing algorithms. Ultimately, it showcases that Quantum Monte Carlo isn't just a numerical tool—it's an expedition that reveals the hidden facets of the quantum world. Part of IOP Series in Quantum Technology. Key features • Accompanying code and worked examples of how an algorithm can be coded and tested. • What makes Quantum Monte Carlo superior and just as importantly, what breaks it. • Teaches statistical physics and quantum physics in parallel. • Includes detailed mathematical derivations that won’t leave blind spots. • Emphasises Quantum Monte Carlo as a tool of visualizing quantum mechanics
This book focuses on the diffusion and path-integral quantum Monte Carlo methods in many-body physics and provides a concise but complete introduction to the Metropolis algorithm and its applications. Several quantum many-body systems are analyzed within and studied in detail. The book includes exercises to help digest the materials covered. It can be used as a tutorial to learn the diffusion and path-integral Monte Carlo or a recipe for developing new research. Two complete Java programs are included and ready for download and adoption.
Monte Carlo methods have been very prominent in computer simulation of various systems in physics, chemistry, biology, and materials science. This book focuses on the discussion and path-integral quantum Monte Carlo methods in many-body physics and provides a concise but complete introduction to the Metropolis algorithm and its applications in these two techniques. To explore the schemes in clarity, several quantum many-body systems are analysed and studied in detail. The book includes exercises to help digest the materials covered. It can be used as a tutorial to learn the discussion and path-integral Monte Carlo or a recipe for developing new research in the reader's own area. Two complete Java programs, one for the discussion Monte Carlo of 4He clusters on a graphite surface and the other for the path-integral Monte Carlo of cold atoms in a potential trap, are ready for download and adoption.
Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference for students and researchers working in condensed matter theory or those interested in advanced numerical methods for electronic simulation.
Monte Carlo methods have been very prominent in computer simulation of various systems in physics, chemistry, biology, and materials science. This book focuses on the discussion and path-integral quantum Monte Carlo methods in many-body physics and provides a concise but complete introduction to the Metropolis algorithm and its applications in these two techniques. To explore the schemes in clarity, several quantum many-body systems are analysed and studied in detail. The book includes exercises to help digest the materials covered. It can be used as a tutorial to learn the discussion and path-integral Monte Carlo or a recipe for developing new research in the reader's own area. Two complete Java programs, one for the discussion Monte Carlo of 4He clusters on a graphite surface and the other for the path-integral Monte Carlo of cold atoms in a potential trap, are ready for download and adoption.
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.