Quantum Monte Carlo Methods: Algorithms for Lattice Models
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.
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Fermion ground state methods
Appendix A Alias method
Appendix F Thoulesss theorem
Appendix H Multielectron propagator
Toward zero temperature
Applications to Bosonic systems
Variational Monte Carlo
Continuoustime auxiliaryfield algorithm
Appendix N Correlated sampling
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approximation auxiliary fields average basis block Bosonic chapter classical cluster compute continuous-time convergence defined density detailed balance determinant method diagonal discrete discuss distribution eigenstates eigenvalue electrons energy entropy equation estimate example expectation value exponential factor Fermion finite finite-temperature flip Gaussian graph element Green’s function Hamiltonian Hubbard-Stratonovich transformation imaginary-time impurity model interaction interval inverse Ising model lattice linear loop loop/cluster Markov chain matrix elements Metropolis algorithm Monte Carlo algorithms Monte Carlo method Monte Carlo simulation noninteracting obtain operators pair parameters partition function phase space power method procedure processor propagation quantum Monte Carlo quantum spin random number random variable result sampling Section sign problem Slater determinant solution statistical step stochastic temperature theorem transition probability update variance variational Monte Carlo vector vertex vertices walker weak-coupling weight world-line worm algorithm XY model zero