High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons

Christiane Lemieux Monte Carlo and Quasi - Monte Carlo Sampling

Efficient Monte Carlo sampling by parallel marginalization.

Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper, a method is proposed to overcome this difficulty. The method utilizes information from rapidly equilibrating coarse Markov chains that sample marginal distributions of the full system. This is accomplished th...

Microcanonical Cluster Monte Carlo

I propose a numerical simulation algorithm for statistical systems which combines a microcanonical transfer of energy with global changes in clusters of spins. The advantages of the cluster approach near a critical point augment the speed increases associated with multi-spin coding in the mi-crocanonical approach. The method also provides a limited ability to tune the average cluster size.

Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent

In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the convergence is measured in the Wasserstein distance and provide further insights on the very tight relations between, on the one hand, the Langevin Monte Carlo fo...

Quantum Monte Carlo method in details

This identity allows to map interacting fermion system onto the system of noninteracting fermions coupled with fluctuating auxilary field. One uses a path integral formulation of a problem to eliminate the interaction term. We divide the imaginary time interbal [0, β] into Lequal subintervals of width ∆τ : L∆τ = β. After doing that we can rewrite equation for the partitionfunction Z as: Z = Tre...