Integrable spin systems with long-range interactions
type: Item
instance of: scholarly article
title: Integrable spin systems with long-range interactions
zbMATH Open document ID: 0768.58046
DOI: 10.1016/0960-0779(92)90029-M
author: Kazuhiro Hikami
author: Miki Wadati
author: P. P. Kulish
published in: Chaos, Solitons and Fractals
publication date: 1993-01-18T00:00:00Z
review text: A method to construct spin Hamiltonians from the \(R\)-matrix is presented. These Hamiltonians describe quantum spin chains where all spins interact through long-range pairwise interactions. The Yang-Baxter relation is considered as a sufficient condition of integrability and then it is proven that the inhomogeneous \(R\)-matrices give integrable spin chains with long-range interactions. The explicit relation between the Hamiltonian and the \(R\)-matrix is obtained and then some applications to various models including spin-1/2 and spin-1 cases are presented. Based on the method previous developed, the integrability of the Haldane-Shastry model and its extension is discussed.
Mathematics Subject Classification ID: 37N99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 81U20
Mathematics Subject Classification ID: 81Q99
zbMATH DE Number: 86304
zbMATH Keywords: integrable system
zbMATH Keywords: spin Hamiltonians
zbMATH Keywords: \(R\)-matrix
zbMATH Keywords: quantum spin chains
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
cites work: Q3324796
cites work: Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
cites work: Theory of nonlinear lattices
cites work: Three integrable Hamiltonian systems connected with isospectral deformations
cites work: Quantum version of the method of inverse scattering problem
cites work: New factorized \(S\)-matrix and its application to exactly solvable \(q\)-state model. I., II.
cites work: Non-abelian Stokes formula
cites work: Quantum R matrix for the generalized Toda system
cites work: Current algebras and Wess-Zumino model in two dimensions
cites work: On the connection between the one-dimensional \(S=1/2\) Heisenberg chain and Haldane-Shastry model
cites work: Solutions of the classical Yang-Baxter equation for simple Lie algebras
description: scientific article; zbMATH DE number 86304