Computer implementation of the Kerov-Kirillov-Reshetikhin algorithm
The Kerov-Kirillov-Reshetikhin (KKR) algorithm establishes a bijection between semistandard Weyl tableaux of the shape lambda and weight mu and rigged string configurations of type (lambda,mu). 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 manlier. Program summary Program title: KKR algorithm C Catalogue identifier: AELQ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 974 No. of bytes in distributed program, including test data, etc.: 11 118 Distribution format: tar.gz Programming language: Maple Computer: PC Operating system: Windows, Linux RAM: 1 GB Classification: 2.7, 4.2 Nature 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 b(irr) of the Schur-Weyl duality all highest weight states vertical bar lambda t(hw)y > with respect to the unitary group U(n) and generates a rigged string configurations vertical bar , {J}> = KKR(vertical bar lambda t(hw)y >) for each y is an element of SYT(lambda). Running time: The running time is about 1 ms. Reference: [1] S. Veigneau, Algebraic Combinatorics Environment for the computer algebra system, User's Reference Manual, Version 3.0 98-11, Universite de Marne-la-Valle, Institut Gaspard-Monge, CNRS, 1998. (C) 2012 Elsevier B.V. All rights reserved.
rigged string configuration kkr algorithm one-dimensional heisenberg magnet weyl tableau schur-weyl basis