Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates

In the reactor design and analysis, there is often a need to calculate the effects caused by perturbations of temperature, components and even structure of reactors on reactivity. And in sensitivity studies, uncertainty analysis of target quantities and unclear data adjustment, perturbation calculations are also widely used. To meet the need of different types of reactors (complex, multidimensional systems), Monte Carlo perturbation methods have been developed. In this paper, several kinds of perturbation methods are investigated. Specially, differential operator sampling method and correlated tracking method are discussed in details. MCNP’s perturbation calculation capability is discussed by calculating certain problems, from which some conclusions are obtained on the capabilities of the differential operator sampling method used in the perturbation calculation model of MCNP. Also, a code using correlated tracking method has been developed to solve certain problems with cross-section changes, and the results generated by this code agree with the results generated by straightforward Monte Carlo techniques.

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Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

Annual Review of Condensed Matter Physics ◽

10.1146/annurev-conmatphys-033117-054307 ◽

2019 ◽

Vol 10 (1) ◽

pp. 337-356 ◽

Cited By ~ 23

Author(s):

Zi-Xiang Li ◽

Hong Yao

Keyword(s):

Monte Carlo ◽

Quantum Monte Carlo ◽

Hot Spot ◽

High Temperature Superconductors ◽

System Size ◽

Many Body ◽

Broken Symmetries ◽

Sign Problem ◽

Universal Quantum ◽

Many Body Systems

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

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GLOBAL MINIMA FOR PdN (N = 5–80) CLUSTERS DESCRIBED BY SUTTON–CHEN POTENTIAL

International Journal of Modern Physics C ◽

10.1142/s0129183107011376 ◽

2007 ◽

Vol 18 (08) ◽

pp. 1351-1359 ◽

Cited By ~ 6

Author(s):

HAYDAR ARSLAN

Keyword(s):

Monte Carlo ◽

Energy Surface ◽

Central Atom ◽

Low Energy ◽

Global Minima ◽

Many Body ◽

Pd Clusters ◽

Body Potential ◽

Basin Hopping ◽

Theoretical Results

The structure and energetics of Pd N (N = 5–80) clusters have been studied extensively by a Monte Carlo method based on Sutton–Chen many-body potential. The basin-hopping algorithm is used to find the low-energy minima on the potential energy surface for each nuclearity. A variety of structure types (icosahedral, decahedral and fcc closed-packed) are observed for Pd clusters. Some of the icosahedral global minima do not have a central atom. The resulting structures have been compared with the previous theoretical results.

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