TY - CHAP

T1 - Variational and diffusion monte carlo approaches to the nuclear few- and many-body problem

AU - Pederiva, Francesco

AU - Roggero, Alessandro

AU - Schmidt, Kevin

N1 - Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - We review Quantum Monte Carlo methods, a class of stochastic methods allowing for solving the many-body Schrödinger equation for an arbitrary Hamiltonian. The basic elements of the stochastic integration theory are first presented, followed by the implementation to the variational solution of the quantum many-body problem. Projection algorithms are then introduced, beginning with a formulation in coordinate space for central potentials, in order to illustrate the fundamental ideas. The extension to Hamiltonians with an explicit dependence on the spin-isospin degrees of freedom is then presented by making use of auxiliary fields (Auxiliary Field Diffusion Monte Carlo, AFDMC). Finally, we present the Configuration Interaction Monte Carlo algorithm (CIMC) a method to compute the ground state of general, local or non-local, Hamiltonians based on the configuration space sampling.

AB - We review Quantum Monte Carlo methods, a class of stochastic methods allowing for solving the many-body Schrödinger equation for an arbitrary Hamiltonian. The basic elements of the stochastic integration theory are first presented, followed by the implementation to the variational solution of the quantum many-body problem. Projection algorithms are then introduced, beginning with a formulation in coordinate space for central potentials, in order to illustrate the fundamental ideas. The extension to Hamiltonians with an explicit dependence on the spin-isospin degrees of freedom is then presented by making use of auxiliary fields (Auxiliary Field Diffusion Monte Carlo, AFDMC). Finally, we present the Configuration Interaction Monte Carlo algorithm (CIMC) a method to compute the ground state of general, local or non-local, Hamiltonians based on the configuration space sampling.

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U2 - 10.1007/978-3-319-53336-0_9

DO - 10.1007/978-3-319-53336-0_9

M3 - Chapter

AN - SCOPUS:85019174106

T3 - Lecture Notes in Physics

SP - 401

EP - 476

BT - Lecture Notes in Physics

PB - Springer Verlag

ER -