As an intrinsically unbiased method, the quantum Monte Carlo (QMC) method is of unique importance in simulating interacting systems. Although QMC often suffers from notorious sign problem, problem models may be mitigated by finding better choices simulation scheme. However, a general framework for identifying optimal schemes has been lacking. Here, we propose using automatic differentiation to ...

This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting k...

It is remarkable how the Fröhlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since ∼ 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-ana...

We have successfully grown sizable single crystals of La2Cu1−z(Zn,Mg)zO4 with up to nearly half of the magnetic Cu sites replaced by non-magnetic Zn and Mg. Neutron scattering, SQUID magnetometry, and complementary quantum Monte Carlo (QMC) simulations demonstrate that this material is an excellent model system for the study of site percolation of the square-lattice Heisenberg antiferromagnet (...

Bose polarons, quasiparticles composed of mobile impurities surrounded by cold gas, can experience strong interactions mediated the many-body environment and form bipolaron bound states. Here we present a detailed study heavy polarons in one-dimensional gas formulating nonperturbative theory complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson ...

Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting of the properties of matter from fundamental principles. By solving the Schrödinger equation through a stochastic projection, it achieves the greatest accuracy and reliability of methods available for physical systems containing more than a few quantum particles. QMC enjoys scaling ...

We have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC, based on maximally localized Wannier orbitals (MLWO), but has the advantage of greater simplicity. The technique we propose draws on methods recently develope...

In this paper advanced variance-based algorithms for global sensitivity analysis are studied. We consider efficient algorithms: Monte Carlo, quasi-Monte Carlo (QMC) and scrambled quasi-Monte Carlo algorithms based on Sobol sequences. Low discrepancy ΛΠτ Sobol sequences are considered as a basis. Two other approaches are also analyzed. The first one is an efficient Monte Carlo (MC) algorithm for...

The perturbatively selected configuration interaction scheme (CIPSI) is particularly effective in constructing determinantal expansions for quantum Monte Carlo (QMC) simulations with Jastrow–Slater wave functions: fast and smooth convergence of ground-state properties balanced descriptions ground excited states different symmetries have been reported. In particular, accurate excitation energies...