Computer implementation of the Kerov-Kirillov-Reshetikhin algorithm

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• 作者：P. Jakubczyk^a ; ^{pjakub@univ.rzeszow.pl} ; A. Wal^a ; D. Jakubczyk^b ; T. Lulek^c
• 关键词：KKR algorithm ; Weyl tableau ; Rigged string configuration ; Schur&ndash ; Weyl basis ; One-dimensional Heisenberg magnet
• 刊名：Computer Physics Communications
• 出版年：2012
• 期刊代码：30_00104655
• 类别：cp
• 出版时间：June, 2012
• 卷：183
• 期：6
• 页码：1354-1362
• 文件大小：322 K

摘要

The Kerov-Kirillov-Reshetikhin (KKR) algorithm establishes a bijection between semistandard Weyl tableaux of the shape 位 and weight 渭 and rigged string configurations of type . 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 summary

Program title: KKR algorithm

Catalogue identifier: AELQ_v1_0

Program summary URL:

Program obtainable from: CPC Program Library, Queen始s University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence,

No. of lines in distributed program, including test data, etc.: 974

No. of bytes in distributed program, including test data, etc.: 11鈥?18

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 of the Schur-Weyl duality all highest weight states | with respect to the unitary group and generates a rigged string configurations for each .

Running time: The running time is about 1 ms.

Reference:

[1]

S. Veigneau, Algebraic Combinatorics Environment for the computer algebra system, User始s Reference Manual, Version 3.0 98-11, Universit茅 de Marne-la-Vall茅, Institut Gaspard-Monge, CNRS, 1998.