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We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…
We develop a perturbative renormalization-group method in real time to describe nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We include energy broadening and dissipation and develop a…
This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo…
Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and…
We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory…
We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by…
In this paper, we solve quantum many-body problem by propagating ensembles of trajectories and guiding waves in physical space. We introduce the 'effective potential' correction within the recently proposed time-dependent quantum Monte…
Non-Hermitian quantum systems exhibit unique properties and hold significant promise for diverse applications, yet their dynamical simulation poses a particular challenge due to intrinsic openness and non-unitary evolution. Here, we…
Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
In the absence of a fermion sign problem, auxiliary field (or determinantal) quantum Monte Carlo (DQMC) approaches have long been the numerical method of choice for unbiased, large-scale simulations of interacting many-fermion systems. More…
We develop the impurity lattice Monte Carlo formalism, for the case of two distinguishable impurities in a bath of polarized fermions. The majority particles are treated as explicit degrees of freedom, while the impurities are described by…
Auxiliary-field quantum Monte Carlo methods enable the calculation of thermal and ground state properties of correlated quantum many-body systems in model spaces that are many orders of magnitude larger than those that can be treated by…
We present a method based on the Path Integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose…
In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schr\"odinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic…
A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier…
We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…
We study the interacting quantum dot coupled to the normal and superconducting leads by means of a continuous-time quantum Monte Carlo method in the Keldysh-Nambu formalism. Deducing the steady current through the quantum dot under a finite…
We develop a real-time Full Configuration Interaction Quantum Monte Carlo approach for the modeling of driven-dissipative open quantum systems. The method enables stochastic sampling of the Liouville-von-Neumann time evolution of the…