Related papers: Recent Developments of World-Line Monte Carlo Meth…
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.…
In this article we review some of recent results on higher order quasi-Monte Carlo (HoQMC) methods. After a seminal work by Dick (2007, 2008) who originally introduced the concept of HoQMC, there have been significant theoretical progresses…
The Fermi gas at unitarity is a particularly interesting system of cold atoms, being dilute and strongly interacting at the same time. It can be studied non-perturbatively with Monte Carlo methods, like the recently developed worm…
From basic considerations of the Lie group that preserves a target probability measure, we derive the Barker, Metropolis, and ensemble Markov chain Monte Carlo (MCMC) algorithms, as well as variants of waste-recycling Metropolis-Hastings…
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical…
Quantum Monte Carlo (QMC) methods are powerful approaches for solving electronic structure problems. Although they often provide high-accuracy solutions, the precision of most QMC methods is ultimately limited by a trial wave function that…
We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths, whose dynamics are described by integro-differential equations. The first approach can be considered as a reformulation of Dyson series, and…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
Reverse Monte Carlo (RMC) is an algorithm that incorporates stochastic modification of the action as part of the process that updates the fields in a Monte Carlo simulation. Such update moves have the potential of lowering or eliminating…
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…
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…
We present a Markov-chain Monte Carlo algorithm of "worm"type that correctly simulates the O(n) loop model on any (finite and connected) bipartite cubic graph, for any real n>0, and any edge weight, including the fully-packed limit of…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the…
The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis-Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov…
This is a book chapter soon to appear (2002) in the "Handbook for Numerical Analysis" volume dedicated to "Computational Chemistry" edited by Claude Le Bris. The series editors are P.G. Ciarlet and J. L. Lions. [North Holland/Elservier].…
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.
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…