Multi-cell Monte Carlo method for phase prediction

Released-phase quantum Monte Carlo method

The correlation function Monte Carlo method for calculating ground and excited state properties is extended to complex Hamiltonians and used to calculate the spectrum of neutral helium in a wide range of magnetic fields, a system of particular interest in astrophysics. Correlation functions in imaginary time are evaluated for a set of trial functions over a random walk whose dynamics is governe...

Multi-way Monte Carlo Method for Linear Systems

We study the Monte Carlo method for solving a linear system of the form x = Hx + b. A sufficient condition for the method to work is ‖H‖ < 1, which greatly limits the usability of this method. We improve this condition by proposing a new multi-way Markov random walk, which is a generalization of the standard Markov random walk. Under our new framework we prove that the necessary and sufficient ...

The Monte-Carlo Method

The Monte Carlo Method

The Monte Carlo method is often referred to as a ‘computer experiment’. One might think of this as a way of conveying the fact that the output of simulations is not an equation, as in conventional theory. Instead, numbers appear on the computer screen in somewhat the same way that numbers appear on a measuring device in the laboratory. Thus there is the implication that somehow simulations are ...

Monte Carlo Simulation Method

Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path Integral Monte Carlo are the most accurate and general methods for computing total electronic energies. We will review methods we have developed to perform QMC for the electrons coupled to another MC simulation for the ions. In this method, one estimates the Born-Oppenheimer energy E(Z) where Z repr...