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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_0Distribution 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 b of the Schur-Weyl duality all highest weight states |λ_{irr}t⟩ with respect to the unitary group _{hw}yU(n) and generates a rigged string configurations |νbar,{J}⟩ = KKR(|λt⟩) for each _{hw}yy ∈ SYT(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. |

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