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Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
The efficiency of statistical sampling in broad-histogram Monte Carlo simulations can be considerably improved by optimizing the simulated extended ensemble for fastest equilibration. Here we describe how a recently developed feedback…
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…
By including elements of the density matrix formalism, the semiclassical ensemble Monte Carlo method for carrier transport is extended to incorporate incoherent tunneling, known to play an important role in quantum cascade lasers (QCLs). In…
We consider the random transverse-field Ising model in $d=3$ dimensions with long-range ferromagnetic interactions which decay as a power $\alpha > d$ with the distance. Using a variant of the strong disorder renormalization group method we…
Monte-Carlo techniques are standard numerical tools for exploring non-Gaussian and multivariate likelihoods. Many variants of the original Metropolis-Hastings algorithm have been proposed to increase the sampling efficiency. Motivated by…
We consider the Ising model on a small-world network, where the long-range interaction strength $J_2$ is in general different from the local interaction strength $J_1$, and examine its relaxation behaviors as well as phase transitions. As…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix…
We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo…
We study one-dimensional quantum gases in continuous space with cavity-mediated infinite-range interactions using variational and diffusion Monte Carlo methods. Starting from the exact two-body solution, we construct a non-translationally…
Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional…
We use quantum Monte Carlo methods and various analytic approximations to solve the Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above…
Non-stoquastic Hamiltonians have both positive and negative signs in off-diagonal elements in their matrix representation in the standard computational basis and thus cannot be simulated efficiently by the standard quantum Monte Carlo…
We propose a method for simulating the stochastic dynamics of classical spin systems with long-range interactions. The method incorporates the stochastic cutoff (SCO) method, which is originally specialized for simulating equilibrium state,…
In past decades, enormous effort has been expended to develop algorithms and even to construct special-purpose computers in order to efficiently evaluate total energies and forces for long-range-interacting particle systems, with the…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…