A strange five vertex model and multispecies ASEP on a ring
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| Format: | Preprint |
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2024
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| author | Kuniba, Atsuo Okado, Masato Scrimshaw, Travis |
| author_facet | Kuniba, Atsuo Okado, Masato Scrimshaw, Travis |
| contents | We revisit the problem of constructing the stationary states of the multispecies asymmetric simple exclusion process on a one-dimensional periodic lattice. Central to our approach is a quantum oscillator weighted five vertex model which features a strange weight conservation distinct from the conventional one. Our results clarify the interrelations among several known results and refine their derivations. For instance, the stationary probability derived from the multiline queue construction by Martin (2020) and Corteel--Mandelshtam--Williams (2022) is identified with the partition function of a three-dimensional system. The matrix product operators by Prolhac--Evans--Mallick (2009) acquire a natural diagrammatic interpretation as corner transfer matrices (CTM). The origin of their recursive tensor structure, as questioned by Aggarwal--Nicoletti--Petrov (2023), is revealed through the CTM diagrams. Finally, the derivation of the Zamolodchikov--Faddeev algebra by Cantini--de Gier--Wheeler (2015) is made intrinsic by elucidating its precise connection to a solution to the Yang--Baxter equation originating from quantum group representations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_12092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A strange five vertex model and multispecies ASEP on a ring Kuniba, Atsuo Okado, Masato Scrimshaw, Travis Mathematical Physics Combinatorics Probability Quantum Algebra 81R50, 60C99 We revisit the problem of constructing the stationary states of the multispecies asymmetric simple exclusion process on a one-dimensional periodic lattice. Central to our approach is a quantum oscillator weighted five vertex model which features a strange weight conservation distinct from the conventional one. Our results clarify the interrelations among several known results and refine their derivations. For instance, the stationary probability derived from the multiline queue construction by Martin (2020) and Corteel--Mandelshtam--Williams (2022) is identified with the partition function of a three-dimensional system. The matrix product operators by Prolhac--Evans--Mallick (2009) acquire a natural diagrammatic interpretation as corner transfer matrices (CTM). The origin of their recursive tensor structure, as questioned by Aggarwal--Nicoletti--Petrov (2023), is revealed through the CTM diagrams. Finally, the derivation of the Zamolodchikov--Faddeev algebra by Cantini--de Gier--Wheeler (2015) is made intrinsic by elucidating its precise connection to a solution to the Yang--Baxter equation originating from quantum group representations. |
| title | A strange five vertex model and multispecies ASEP on a ring |
| topic | Mathematical Physics Combinatorics Probability Quantum Algebra 81R50, 60C99 |
| url | https://arxiv.org/abs/2408.12092 |