Related papers: Tethered Monte Carlo: computing the effective pote…
We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a…
An efficient continuous-time path-integral Quantum Monte Carlo algorithm for the lattice polaron is presented. It is based on Feynman's integration of phonons and subsequent simulation of the resulting single-particle self-interacting…
Simulating long-range interacting systems is a challenging task due to its computational complexity that the computational effort for each local update is of order $\cal{O}$$(N)$, where $N$ is the size of system. Recently, a technique,…
A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…
We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects. The computational efficiency is investigated on test problems given by tight-binding models…
This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in…
We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
A rich literature has been produced on the quantum states of atoms and molecules confined into infinite potential wells with a specified symmetry. Apart from their interest as basic quantum systems, confined atoms and molecules are useful…
We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate…
A quantum Monte Carlo method with non-local update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and…
We propose a new quantum Monte Carlo algorithm which realizes a relaxation intrinsic to the original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation $\tau\sim \xi^z$ and is independent of the Trotter number.…
We present the ground state extension of the efficient quantum Monte Carlo algorithm for lattice fermions of arXiv:1411.0683. Based on continuous-time expansion of imaginary-time projection operator, the algorithm is free of systematic…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives…