Computer implementation of the Kerov–Kirillov–Reshetikhin algorithm

Abstract

The Kerov–Kirillov–Reshetikhin (KKR) algorithm establishes a bijection between semistandard Weyl tableaux of the shape λ and weight μ and rigged string configurations of type (λ,μ). This algorithm can be applied to Heisenberg magnetic chains and their generalisations by use of Schur–Weyl duality, and gives a way to classify all eigenstates of the chain in a methodological manner. Program summaryProgram title: KKR algorithmCatalogue identifier: AELQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELQ_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.: 974No. of bytes in distributed program, including test data, etc.: 11 118Distribution format: tar.gzProgramming language: MapleComputer: PCOperating system: Windows, LinuxRAM: 1 GBClassification: 2.7, 4.2Nature of problem: The method of classification of all eigenstates and eigenvalues is given for the generalised model of the one-dimensional Heisenberg magnet consisting of N nodes.Solution method: We use a prolongation of the RSK bijection [1] to the set of all eigenstates of an integrable model, in terms of rigged string configurations. More specifically, one selects from the irreducible basis birr of the Schur–Weyl duality all highest weight states |λthwy〉 with respect to the unitary group U(n) and generates a rigged string configurations |ν→,{J}〉=KKR(|λthwy〉) for each y∈SYT(λ).Running time: The running time is about 1 ms.Reference:[1]S. Veigneau, Algebraic Combinatorics Environment for the computer algebra system, Userʼs Reference Manual, Version 3.0 98-11, Université de Marne-la-Vallé, Institut Gaspard-Monge, CNRS, 1998.