Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory

被引：1

作者：

Hartung, Tobias ^{[1
,2
]}

Jansen, Karl ^{[3
]}

Kuo, Frances Y. ^{[4
]}

Leoevey, Hernan ^{[5
]}

Nuyens, Dirk ^{[6
]}

Sloan, Ian H. ^{[4
]}

机构：

[1] Cyprus Inst, Computat Based Sci & Technol Res Ctr, 20 Konstantinou Kavafi St, CY-2121 Nicosia, Cyprus

[2] Kings Coll London, Dept Math, London WC2R 2LS, England

[3] DESY Zeuthen, NIC, Platanenallee 6, D-15738 Zeuthen, Germany

[4] UNSW Sydney, Sch Math & Stat, Sydney, NSW 2052, Australia

[5] AXPO Trading & Sales, Struct Energy Trading, Pk Str 23, D-5400 Baden Baden, Germany

[6] Katholieke Univ Leuven, Dept Comp Sci, Celestijnenlaan 200A, B-3001 Leuven, Belgium

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2021年 / 443卷

基金：

澳大利亚研究理事会;

关键词：

Lattice cubature; Quasi-Monte Carlo; Recursive integration; Lattice gauge theory; Quantum physics; RECURSIVE INTEGRATION METHODOLOGIES; MONTE; SYSTEMS;

D O I：

10.1016/j.jcp.2021.110527

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings , motivated by models in lattice gauge theory from quantum field theory. A novel element of this work is the potential benefit in using lattice cubature rules. The group structure within lattice rules combined with the special structure in the physics integrands may allow efficient computations based on Fast Fourier Transforms. Applications to the quantum mechanical rotor and compact U(1) lattice gauge theory in two and three dimensions are considered. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：24

共 30 条

[1] Overcoming the sign problem in one-dimensional QCD by new integration rules with polynomial exactness [J].

Ammon, A. ;

Hartung, T. ;

Jansen, K. ;

Leoevey, H. ;

Volmer, J. .

PHYSICAL REVIEW D, 2016, 94 (11)

[2] On the efficient numerical solution of lattice systems with low-order couplings [J].

Ammon, A. ;

Genz, A. ;

Hartung, T. ;

Jansen, K. ;

Leoevey, H. ;

Volmer, J. .

COMPUTER PHYSICS COMMUNICATIONS, 2016, 198 :71-81

[3]

Ammon A., 2016, LATTICE 2016, P334

[4]

Ammon A., 2014, LATTICE 2013

[5] GAUGE FIELDS ON A LATTICE .3. STRONG-COUPLING EXPANSIONS AND TRANSITION POINTS [J].

BALIAN, R ;

DROUFFE, JM ;

ITZYKSON, C .

PHYSICAL REVIEW D, 1975, 11 (08) :2104-2119

[6] Topological lattice actions [J].

Bietenholz, W. ;

Gerber, U. ;

Pepe, M. ;

Wiese, U. -J. .

JOURNAL OF HIGH ENERGY PHYSICS, 2010, (12)

[7] Perfect lattice topology: The quantum rotor as a test case [J].

Bietenholz, W ;

Brower, R ;

Chandrasekharan, S ;

Wiese, UJ .

PHYSICS LETTERS B, 1997, 407 (3-4) :283-289

[8] A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec [J].

Borowka, S. ;

Heinrich, G. ;

Jahn, S. ;

Jones, S. P. ;

Kerner, M. ;

Schlenk, J. .

COMPUTER PHYSICS COMMUNICATIONS, 2019, 240 :120-137

[9]

Bungartz HJ, 2004, ACT NUMERIC, V13, P147, DOI 10.1017/S0962492904000182

[10]

Caflisch R., 1997, J. Comput. Finance, V1, P27, DOI [10.21314/JCF.1997.005, DOI 10.21314/JCF.1997.005]

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