We study hard-core bosons on the honeycomb lattice in presence of anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte Carlo (QMC) technique, we extract phase diagram model terms filling and anisotropy. At half-filling find dimer insulator near maximum anisotropy that is characterized by finite topological entanglement entropy $ln(2)/2$, indicative fractional Hall state fo...

Quasi-Monte Carlo (QMC) sampling has been developed for integration over [0, 1] where it has superior accuracy to Monte Carlo (MC) for integrands of bounded variation. Scrambled net quadrature gives allows replication based error estimation for QMC with at least the same accuracy and for smooth enough integrands even better accuracy than plain QMC. Integration over triangles, spheres, disks and...

Continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting the properties of matter from fundamental principles. By solving the manybody Schrödinger equation through a stochastic projection, it achieves greater accuracy than mean-field methods and better scalability than quantum chemical methods, enabling scientific discovery across a broad spectrum of disciplines. T...

In the past decade, quasi-Monte Carlo (QMC) method has become an important numerical tool in computational finance. This is driven, in part, by the sophistication of the models and, in part, by the complexity of the derivative securities. In this paper, we consider an enhanced QMC method recently proposed by Imai and Tan (2009). This method is known as the generalized linear transformation (GLT...

We present a pedagogical discussion of the the Hirsch-Fye and Continuous time Quantum Monte Carlo (QMC) algorithms which may be used to study a correlated cluster embedded in an uncorrelated host, or used to solve the cluster problem in dynamical mean field theory (DMFT) or its cluster extensions. The basic algorithms are discussed, together with methods for efficient measurments and the modifi...

We report an analytical representation of the correlation energy ec(rs, zeta) for a uniform electron gas (UEG), where rs is Seitz radius or density parameter and zeta relative spin polarization. The new functional, called W20, constructed to capture known high-density low-density limit (for = 0 1) without any fitting parameters. comparative assessment against recent quantum Monte Carlo (QMC) re...

The spectral properties of La1−xSrxTiO3, a doped Mott insulator with strong Coulomb correlations, are calculated with the ab initio computational scheme LDA+DMFT(QMC). It starts from the non-interacting electronic band structure as calculated by the local density approximation (LDA), and introduces the missing correlations by the dynamical mean-field theory (DMFT), using numerically exact quant...

[0,1]d f(x)dx. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of O(n) from n independent random function evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully equispaced evaluation points can attain the rate O(n) for any ε > 0 and randomized QMC (RQMC) can attain the RMSE O(n), both under mild conditions on f . Classical variance reduction meth...

Quasi-Monte Carlo (QMC) methods for high dimensional integrals have been well studied for the unit cube. Sloan and Woźniakowski [18] partially solve the question of why they are significantly more efficient than Monte carlo methods. Kuo and Sloan [9] prove similar results for integration over product of spheres. We study the QMC tractability of integrals of functions defined over the product of...

In performing statistical studies in simulation science, it is often necessary to estimate the value of an integral of a function that is based on a simulation calculation. Because simulations tend to be costly in terms of computer time and resources, the ability to accurately estimate integrals with a minimum number of function evaluations is a critical issue in evaluating simulation codes. Th...