R-matrix-valued Lax pairs and long-range spin chains
| Autor: | I. Sechin, A. V. Zotov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics Integrable system Scalar (mathematics) FOS: Physical sciences 01 natural sciences Condensed Matter - Strongly Correlated Electrons 0103 physical sciences 010306 general physics Anisotropy Commutative property Quantum Mathematical Physics R-matrix Mathematical physics Physics Strongly Correlated Electrons (cond-mat.str-el) Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics (math-ph) lcsh:QC1-999 Nonlinear Sciences::Exactly Solvable and Integrable Systems High Energy Physics - Theory (hep-th) Condensed Matter::Strongly Correlated Electrons 010307 mathematical physics Exactly Solvable and Integrable Systems (nlin.SI) Trigonometry lcsh:Physics |
| Zdroj: | Physics Letters B, Vol 781, Iss, Pp 1-7 (2018) Physics Letters |
| ISSN: | 0370-2693 |
| Popis: | In this paper we discuss $R$-matrix-valued Lax pairs for ${\rm sl}_N$ Calogero-Moser model and their relation to integrable quantum long-range spin chains of the Haldane-Shastry-Inozemtsev type. First, we construct the $R$-matrix-valued Lax pairs for the third flow of the classical Calogero-Moser model. Then we notice that the scalar parts (in the auxiliary space) of the $M$-matrices corresponding to the second and third flows have form of special spin exchange operators. The freezing trick restricts them to quantum Hamiltonians of long-range spin chains. We show that for a special choice of the $R$-matrix these Hamiltonians reproduce those for the Inozemtsev chain. In the general case related to the Baxter's elliptic $R$-matrix we obtain a natural anisotropic extension of the Inozemtsev chain. Commutativity of the Hamiltonians is verified numerically. Trigonometric limits lead to the Haldane-Shastry chains and their anisotropic generalizations. 12 pages, Introduction added, minor corrections |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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