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The hybrid Monte Carlo (HMC) algorithm is a ubiquitous method in computational physics with applications ranging from condensed matter to lattice QCD and beyond. However, HMC simulations often suffer from long autocorrelation times,…
We describe the implementation of the frozen-orbital and downfolding approximations in the auxiliary-field quantum Monte Carlo (AFQMC) method. These approaches can provide significant computational savings compared to fully correlating all…
The temperature dependence of the correlation length, susceptibilities and the magnetic structure factor of the two-dimensional spin-1 square lattice quantum Heisenberg antiferromagnet are computed by the quantum Monte Carlo loop algorithm…
A quantum world-line Monte Carlo method for high-symmetrical quantum models is proposed. Firstly, based on a representation of a partition function using the Matsubara formula, the principle of quantum world-line Monte Carlo methods is…
We present a new Monte Carlo algorithm for simulating quantum spin systems which is able to suppress the negative sign problem. This algorithm has only a linear complexity in the lattice size used for the simulation. A general description…
The antiferromagnetic Heisenberg model on a pyrochlore lattice under external magnetic field is studied by classical Monte Carlo simulation. The model includes bilinear and biquadratic interactions; the latter effectively describes the…
We present a new approach for Monte Carlo simulations of lattice quantum spin systems which is able to eliminate the negative sign problem. Its complexity is linear in the volume of the lattice. Its efficiency is tested on a simple…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate…
The critical properties of the antiferromagnetic Heisenberg model on the three-dimensional stacked-triangular lattice are studied by means of a large-scale Monte Carlo simulation in order to get insight into the controversial issue of the…
By precisely writing down the matrix element of the local Boltzmann operator, we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With current formula, the…
In this paper, we consider the numerical solution of a nonlinear Schrodinger equation with spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule combined with the time-splitting pseudospectral discretization is…
A continuous-time formulation of the Diffusion Monte Carlo method for lattice models is presented. In its simplest version, without the explicit use of trial wavefunctions for importance sampling, the method is an excellent tool for…
We apply the recently developed adaptive ensemble optimization technique to simulate dense Lennard-Jones fluids and a particle-solvent model by broad-histogram Monte Carlo techniques. Equilibration of the simulated fluid is improved by…
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field…
We study a generalized clock model on the simple cubic lattice. The parameter of the model can be tuned such that the amplitude of the leading correction to scaling vanishes. In the main part of the study we simulate the model with $Z_8$…
We present the results of Monte Carlo simulation for a Kondo lattice model in which itinerant electrons interact with Ising spins with spin-ice type easy-axis anisotropy on a pyrochlore lattice. We demonstrate the efficiency of the…