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Although the nonequilibrium relaxation (NER) method has been widely used in Monte Carlo studies on phase transitions in classical spin systems, such studies have been quite limited in quantum phase transitions. The reason is that relaxation…
Hamiltonian Monte Carlo (HMC) is a powerful Markov Chain Monte Carlo (MCMC) method for sampling from complex high-dimensional continuous distributions. However, in many situations it is necessary or desirable to combine HMC with other…
An overview is given over the recently developed and now widely used Monte Carlo algorithms with reduced or eliminated critical slowing down. The basic techniques are overrelaxation, cluster algorithms and multigrid methods. With these…
We review the background of the cluster algorithms in Monte Carlo simulation of statistical physics problems. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local…
We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and…
We present a new non-local updating scheme for quantum Monte Carlo simulations, which conserves particle number and other symmetries. It allows exact symmetry projection and direct evaluation of the equal-time Green's function and other…
Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress…
Cluster expansions for the exponential of local operators are constructed using tensor networks. In contrast to other approaches, the cluster expansion does not break any spatial or internal symmetries and exhibits a very favourable…
Effects of randomness on the spin-1/2 and 1 antiferromagnetic Heisenberg chains are studied using the quantum Monte Carlo method with the continuous-time loop algorithm. We precisely calculated the uniform susceptibility, string order…
We describe a stochastic series expansion (SSE) quantum Monte Carlo method for a two-dimensional S=1/2 XY-model (or, equivalently, hard-core bosons at half-filling) which in addition to the standard pair interaction J includes a…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
Coupled cluster theory is a vital cornerstone of electronic structure theory and is being applied to ever-larger systems. Stochastic approaches to quantum chemistry have grown in importance and offer compelling advantages over traditional…
The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct…
We design an enhanced Event-Chain Monte Carlo algorithm to study 1D quantum dissipative systems, using their bosonized representation. Expressing the bosonized Hamiltonian as a path integral over a scalar field enables the application of…
Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural…
We propose a Monte Carlo method which performs a random walk in energy space using cluster-like collective updates. By imposing that bond probabilities depend continuously on the microcanonical temperature, we obtain dynamic exponents close…
We extend the continuous-time interaction-expansion quantum Monte Carlo method with respect to measuring observables for fermion-boson lattice models. Using generating functionals, we express expectation values involving boson operators,…
Quantum dimer model is a low-energy and efficient model to study quantum spin systems and strong-correlated physics. As a foreseeing step and without loss of generality, we study the classical dimers on square lattice by means of Monte…
The stochastic block model (SBM) is a flexible probabilistic tool that can be used to model interactions between clusters of nodes in a network. However, it does not account for interactions of time varying intensity between clusters. The…
Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each…