Regularization of multi-soliton form factors in sine-Gordon model

Abstract

A general and systematic regularization is developed for the exact solitonic form factors of exponential operators in the (1+1)-dimensional sine-Gordon model by analytical continuation of their integral representations. The procedure is implemented in Mathematica. Test results are shown for four- and six-soliton form factors. Program summaryProgram title: SGFFCatalogue identifier: AEMG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMG_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1462No. of bytes in distributed program, including test data, etc.: 15 488Distribution format: tar.gzProgramming language: Mathematica [1]Computer: PCOperating system: Cross-platformClassification: 7.7, 11.1, 23Nature of problem: The multi-soliton form factors of the sine-Gordon model (relevant in two-dimensional physics) were given only by highly non-trivial integral representation with a limited domain of convergence. Practical applications of the form factors, e.g. calculation of correlation functions in two-dimensional condensed matter systems, were not possible in general.Solution method: Using analytic continuation techniques an efficient algorithm is found and implemented in Mathematica, which provides a general and systematic way to calculate multi-soliton form factors in the sine-Gordon model. The package contains routines to compute the two-, four- and six-soliton form factors.Running time: Strongly dependent on the desired accuracy and the number of solitons. For physical rapidities after an initialization of about 30 s, the calculation of the two-, four- and six-soliton form factors at a single point takes approximately 0.5 s, 2.5 s and 8 s, respectively.Reference:[1]Wolfram Research, Inc., Mathematica Edition: Version 7.0, Wolfram Research, Inc., Champaign, Illinois, 2008.