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[Licence| Download | New Version Template] aelq_v1_0.tar.gz(10 Kbytes)
Manuscript Title: Computer implementation of the Kerov-Kirillov-Reshethikin algorithm
Authors: P. Jakubczyk, A. Wal, D. Jakubczyk, T. Lulek
Program title: KKR algorithm
Catalogue identifier: AELQ_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 183(2012)1354
Programming language: Maple.
Computer: PC.
Operating system: Windows, Linux.
RAM: 1GB bytes
Keywords: KKR algorithm, Classification of states, Bethe Ansatz, Highest weight states, Spin chains.
Classification: 2.7, 4.2.

Nature of problem:
The method of classification of all eigenstates and eigenvalues is given for the generalized 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 |νbar,{J}⟩ = KKR(|λthwy⟩) for each ySYT(λ).

Running time:
The running time is about 1 ms.

References:
[1] S. Veigneau, Algebraic Combinatorics Environment for the computer algebra system, "User's Reference Manual, Version 3.0 98-11", Université de Marne-la- Vallé, Institut Gaspard-Monge, CNRS, 1998.