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Decorated star-triangle relations and exact integrability of the one-dimensional Hubbard model

B. Sriram Shastry

Journal of Statistical PhysicsJan 1, 1988186 citations

Integrability of the one-dimensional hubbard model and related models

修一村上

Jan 1, 19990 citations

Decorated Star-Triangle Relations for the Free-Fermion Model and a New Solvable Bilayer Vertex Model

Masahiro Shiroishi, Miki Wadati

The decorated star-triangle relation (DSTR) discussed by Shastry is extended into the general free-fermion model. Using the trigonometric limit of the DSTR, we construct a new solvable bilayer vertex model. The relation between the DSTR and the tetrahedral Zamolodchikov algebra is discussed.

Journal of the Physical Society of JapanAug 15, 199521 citations

Algebraic and analytic properties of the one-dimensional Hubbard model

Shuichi Murakami

Jan 1, 19970 citations

Integrable Quantum Circuits from the Star-Triangle Relation

Yuan Miao, Eric Vernier

The star-triangle relation plays an important role in the realm of exactly solvable models, offering exact results for classical two-dimensional statistical mechanical models. In this article, we construct integrable quantum circuits using the star-triangle relation. Our construction relies on families of mutually commuting two-parameter transfer matrices for statistical mechanical models solved by the star-triangle relation, and differs from previously known constructions based on Yang-Baxter integrable vertex models. At special value of the spectral parameter, the transfer matrices are mapped into integrable quantum circuits, for which infinite families of local conserved charges can be derived. We demonstrate the construction by giving two examples of circuits acting on a chain of Q− state qudits: Q -state Potts circuits, whose integrability has been conjectured recently by Lotkov et al., and ZQ circuits, which are novel to our knowledge. In the first example, we present for Q=3 a connection to the Zamolodchikov-Fateev 19-vertex model.The star-triangle relation plays an important role in the realm of exactly solvable models, offering exact results for classical two-dimensional statistical mechanical models. In this article, we construct integrable quantum circuits using the star-triangle relation. Our construction relies on families of mutually commuting two-parameter transfer matrices for statistical mechanical models solved by the star-triangle relation, and differs from previously known constructions based on Yang-Baxter integrable vertex models. At special value of the spectral parameter, the transfer matrices are mapped into integrable quantum circuits, for which infinite families of local conserved charges can be derived. We demonstrate the construction by giving two examples of circuits acting on a chain of Q− state qudits: Q -state Potts circuits, whose integrability has been conjectured recently by Lotkov et al., and ZQ circuits, which are novel to our knowledge. In the first example, we present for Q=3 a connection to the Zamolodchikov-Fateev 19-vertex model.

arXiv:2302.12675QuantumNov 3, 202317 citations

Fermionic R -Operator and Integrability of the One-Dimensional Hubbard Model

有希子梅野, Masahiro Shiroishi, Miki Wadati

We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.

arXiv:cond-mat/9806144Journal of the Physical Society of JapanJul 15, 199828 citations

Decorated Star–Triangle Relations and Exact Integrability of the One-Dimensional Hubbard Model

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