Quantized six-vertex model on a torus
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916735826788352 |
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| author | Inoue, Rei Kuniba, Atsuo Terashima, Yuji Yagi, Junya |
| author_facet | Inoue, Rei Kuniba, Atsuo Terashima, Yuji Yagi, Junya |
| contents | We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the homology cycles of the torus, can be defined not only on the square lattice but also on more general graphs. For a class of graphs that we call admissible, we establish the commutativity of the layer transfer matrices by introducing four types of tetrahedron equations and two types of inversion relations. Expanding in the spectral parameters yields a family of commuting quantum Hamiltonians. The quantized six-vertex model can also be reformulated in terms of (quantized) dimer models, and encompasses known integrable systems as special cases, including the free parafermion model and the relativistic Toda chain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_08924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantized six-vertex model on a torus Inoue, Rei Kuniba, Atsuo Terashima, Yuji Yagi, Junya Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics Geometric Topology Quantum Algebra 82B23, 81R12 We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the homology cycles of the torus, can be defined not only on the square lattice but also on more general graphs. For a class of graphs that we call admissible, we establish the commutativity of the layer transfer matrices by introducing four types of tetrahedron equations and two types of inversion relations. Expanding in the spectral parameters yields a family of commuting quantum Hamiltonians. The quantized six-vertex model can also be reformulated in terms of (quantized) dimer models, and encompasses known integrable systems as special cases, including the free parafermion model and the relativistic Toda chain. |
| title | Quantized six-vertex model on a torus |
| topic | Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics Geometric Topology Quantum Algebra 82B23, 81R12 |
| url | https://arxiv.org/abs/2505.08924 |