They
tutorially review the determinantal Quantum Monte Carlo method for
fermionic systems, using the Hubbard model as a case study. Starting
with the basic ingredients of Monte Carlo simulations for classical
systems, they introduce aspects such as importance sampling, sources of
errors, and finite-size scaling analyses. We then set up the
preliminary steps to prepare for the simulations, showing that they are
actually carried out by sampling discrete Hubbard-Stratonovich
auxiliary fields. In this process the Green's function emerges as a
fundamental tool, since it is used in the updating process, and, at the
same time, it is directly related to the quantities probing magnetic,
charge, metallic, and superconducting behaviours. They also discuss the
as yet unresolved "minus-sign problem", and two ways to stabilize the
algorithm at low temperatures.

A
self-contained and tutorial presentation of the diffusion Monte Carlo
method for determining the ground state energy and wave function of
quantum systems is provided. First, the theoretical basis of the method
is derived and then a numerical algorithm is formulated. The algorithm
is applied to determine the ground state of the harmonic oscillator,
the Morse oscillator, the hydrogen atom, and the electronic ground
state of the H2 ion and of the H2 molecule.

They
present a new technics used to develop a new quantum simulation method
which allows to calculate the ground-state expectation values of local
observables without any mixed estimates.

Fermion Nodes Author: David Ceperleylanguage : format:
Ps

This
article discusses the basic properties of the path integral method for
continuum fermions, focusing on the restricted path integral (RPIMC)
approach.

They
review random walks and the quantum Monte Carlo methods used to
simulate the ground state of many-body quantum systems, namely
variational Monte Carlo and projector Monte Carlo.

This
article describes the variational and fixed-node diffusion quantum
Monte Carlo methods and how they may be used to calculate the
properties of many-electron systems.