dorsal/arxiv
View SchemaNon-additive fusion, Hubbard models and non-locality
| Authors | Z. Maassarani |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9908001 |
| URL | https://arxiv.org/abs/solv-int/9908001 |
| DOI | 10.1088/0305-4470/32/49/310 |
| Journal | J. Phys. A 32 (1999) 8691-8703 |
Abstract
In the framework of quantum groups and additive R-matrices, the fusion procedure allows to construct higher-dimensional solutions of the Yang-Baxter equation. These solutions lead to integrable one-dimensional spin-chain Hamiltonians. Here fusion is shown to generalize naturally to non-additive R-matrices, which therefore do not have a quantum group symmetry. This method is then applied to the generalized Hubbard models. Although the resulting integrable models are not as simple as the starting ones, the general structure is that of two spin-(s times s') sl(2) models coupled at the free-fermion point. An important issue is the probable lack of regular points which give local Hamiltonians. This problem is related to the existence of second order zeroes in the unitarity equation, and arises for the XX models of higher spins, the building blocks of the Hubbard models. A possible connection between some Lax operators L and R-matrices is noted.
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"abstract": "In the framework of quantum groups and additive R-matrices, the fusion\nprocedure allows to construct higher-dimensional solutions of the Yang-Baxter\nequation. These solutions lead to integrable one-dimensional spin-chain\nHamiltonians. Here fusion is shown to generalize naturally to non-additive\nR-matrices, which therefore do not have a quantum group symmetry. This method\nis then applied to the generalized Hubbard models. Although the resulting\nintegrable models are not as simple as the starting ones, the general structure\nis that of two spin-(s times s\u0027) sl(2) models coupled at the free-fermion\npoint. An important issue is the probable lack of regular points which give\nlocal Hamiltonians. This problem is related to the existence of second order\nzeroes in the unitarity equation, and arises for the XX models of higher spins,\nthe building blocks of the Hubbard models. A possible connection between some\nLax operators L and R-matrices is noted.",
"arxiv_id": "solv-int/9908001",
"authors": [
"Z. Maassarani"
],
"categories": [
"solv-int",
"cond-mat",
"math-ph",
"math.MP",
"nlin.SI"
],
"doi": "10.1088/0305-4470/32/49/310",
"journal_ref": "J. Phys. A 32 (1999) 8691-8703",
"title": "Non-additive fusion, Hubbard models and non-locality",
"url": "https://arxiv.org/abs/solv-int/9908001"
},
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