Quantum Monte Carlo Methods
Algorithms for Lattice Models

The first textbook to provide a pedagogical examination of the major algorithms used in quantum Monte Carlo simulations.

James Gubernatis (Author), Naoki Kawashima (Author), Philipp Werner (Author)

9781107006423, Cambridge University Press

Hardback, published 2 June 2016

512 pages, 60 b/w illus.
25.3 x 17.9 x 2.6 cm, 2.48 kg

'There's a lot in here but it is explained clearly with many outline algorithms and exercises … I'm sure it will become a standard reference in this area for some time because of the range of … techniques it describes and the care that has gone in to explaining them as clearly as possible given the technical nature of the subject.' Keith A. Benedict, Contemporary Physics

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.

Part I. Monte Carlo Basics: 1. Introduction
2. Monte Carlo basics
3. Data analysis
4. Monte Carlo for classical many-body problems
5. Quantum Monte Carlo primer
Part II. Finite Temperature: 6. Finite-temperature quantum spin algorithms
7. Determinant method
8. Continuous-time impurity solvers
Part III. Zero Temperature: 9. Variational Monte Carlo
10. Power methods
11. Fermion ground state methods
12. Analytic continuation
13. Parallelization.

Subject Areas: Computer science [UY], Computing & information technology [U], Condensed matter physics [liquid state & solid state physics PHFC], Materials / States of matter [PHF], Physics [PH], Mathematics & science [P]