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Gubernatis J., Kawashima N., Werner P. Quantum Monte Carlo Methods: Algorithms for Lattice Models

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Gubernatis J., Kawashima N., Werner P. Quantum Monte Carlo Methods: Algorithms for Lattice Models
Cambridge University Press, UK, 2016. — 502 p. — ISBN-10: 1107006422.
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.
Contents
Monte Carlo basics
Introduction
Monte Carlo basics
Data analysis
Monte Carlo for classical many-body problems
Quantum Monte Carlo primer
Finite temperature
Finite-temperature quantum spin algorithms
Determinant method
Continuous-time impurity solvers
Zero temperature
Variational Monte Carlo
Power methods
Fermion ground state methods
Other topics
Analytic continuation
Parallelization
Appendixes
Alias method
Rejection method
Extended-ensemble methods
Loop/cluster algorithms: SU(N) model
Long-range interactions
Thouless’s theorem
Hubbard-Stratonovich transformations
Multi-electron propagator
Zero temperature determinant method
Anderson impurity model: chain representation
Anderson impurity model: action formulation
Continuous-time auxiliary-field algorithm
Continuous-time determinant algorithm
Correlated sampling
The Bryan algorithm
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