An Overview of Quantum Monte Carlo Methods

@article{Ceperley2010AnOO,
  title={An Overview of Quantum Monte Carlo Methods},
  author={David M. Ceperley},
  journal={Reviews in Mineralogy \& Geochemistry},
  year={2010},
  volume={71},
  pages={129-135}
}
  • D. Ceperley
  • Published 2010
  • Physics
  • Reviews in Mineralogy & Geochemistry
In this brief article, various types of quantum Monte Carlo (QMC) methods are introduced, in particular, those that are applicable to systems in extreme regimes of temperature and pressure. References to longer articles have been given where detailed discussion of applications and algorithms appear. One does QMC for the same reason as one does classical simulations; there is no other method able to treat exactly the quantum many-body problem aside from the direct simulation method where… 

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References

SHOWING 1-10 OF 34 REFERENCES
Quantum Monte Carlo simulations of solids
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. These stochastic
Fixed-node quantum Monte Carlo for molecules
The ground‐state energies of H2, LiH, Li2, and H2O are calculated by a fixed‐node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions
Path integrals in the theory of condensed helium
One of Feynman`s early applications of path integrals was to superfluid {sup 4}He. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of
Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations
We introduce a new stochastic method for calculating ground-state properties of quantum systems. Segments of a Langevin random walk guided by a trial wave function are subject to a Metropolis
Quantum Monte Carlo method using phase-free random walks with slater determinants.
TLDR
A quantum Monte Carlo method for many fermions using random walks in the space of Slater determinants is developed, and the calculated binding energies of dimers and cohesive energy of bulk Si are comparable to the best existing theoretical results.
Monte Carlo simulation of a many-fermion study
The Metropolis Monte Carlo method is used to sample the square of an antisymmetric wave function composed of a product of a Jastrow wave function and a number of Slater determinants. We calculate
Atomic theory of the lambda transition in helium
It is shown from first principles that, in spite of the large interatomic forces, liquid He4 should exhibit a transition analogous to the transition in an ideal Bose-Einstein gas. The exact partition
Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations.
TLDR
A study of hydrogen at pressures higher than molecular dissociation using the coupled electron-ion Monte Carlo method finds disagreement with chemical models, which suggests that a reinvestigation of planetary models--previously constructed using the Saumon-Chabrier-Van Horn equations of state--might be needed.
The penalty method for random walks with uncertain energies
We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed
Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms.
TLDR
Results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas are shown using Hartree-Fock, Slater-Jastrow, and three-body and backflow wave function.
...
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