Characterization of completely X-symmetric factorized S-matrices for a special type of interaction applications to multicomponent field theories

Chudnovsky, D. V.; Chudnovsky, G. V.

doi:10.1016/0375-9601(80)90311-4

Cited by 27 publications

(4 citation statements)

References 8 publications

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“…For a particular choice of the parameters, the solutions with n + 1 A(u) function, we recover the R of the affine Lie algebra A Several particular solutions of the Yang-Baxter equation associated with The 15 -vertex models are known. We can cite, for example, the fifteen-vertex R matrices of Cherednik [42], Babelon [43], Chudnovsky & Chudnovsky [44] and Perk & Schultz [45,46] and [47] (these solutions hold for higher vertex models as well). These R matrices contain fewer parameters than the solutions we found, so that they can be thought of as reductions of a more general solution.…”

Section: Discussionmentioning

confidence: 99%

The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach

Vieira,

Lima-Santos

2020

Preprint

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The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of dierential equations. The derivatives of the R matrix elements, however, can be regarded as independent variables and eliminated from the systems, after which two systems of polynomial equations are obtained in place. In general, these polynomial systems have a non-zero Hilbert dimension, which means that not all elements of the R matrix can be fixed through them. Nevertheless, the remaining unknowns can be found by solving a few number of simple differential equations that arise as consistency conditions of the method. The branches of the solutions can also be easily analyzed by this method, which ensures the uniqueness and generality of the solutions. In this work we considered the Yang-Baxter equation for the (n + 1)(2n + 1)-vertex models with a generalization based on the An−1 symmetry. This differential approach allowed us to solve the Yang-Baxter equation in a systematic way. .

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Section: Discussionmentioning

confidence: 99%

The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach

Vieira,

Lima-Santos

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Several particular solutions of the YBE associated with the 15-vertex models are known. We can cite, for example, the fifteen-vertex R matrices of Cherednik [43], Babelon [44], Chudnovsky and Chudnovsky [45] and Perk and Schultz [46][47][48] (these solutions hold for higher vertex models as well). These R matrices contain fewer parameters than the solutions we found, so they can be thought of as reductions of a more general solution.…”

Section: Solutionmentioning

confidence: 99%

Solutions of the Yang–Baxter equation for (n + 1) (2n + 1)-vertex models using a differential approach

Vieira¹,

Lima-Santos²

2021

J. Stat. Mech.

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The formal derivatives of the Yang–Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the R matrix elements, however, can be regarded as independent variables and eliminated from the systems, after which, two systems of polynomial equations are obtained in their place. In general, these polynomial systems have a non-zero Hilbert dimension, which means that not all elements of the R matrix can be fixed through them. Nevertheless, the remaining unknowns can be found by solving a few simple differential equations that arise as consistency conditions of the method. The branches of the solutions can also be easily analyzed by this method, which ensures the uniqueness and generality of the solutions. In this work, we consider the Yang–Baxter equation for (n + 1) (2n + 1)-vertex models with a generalization based on the A n−1 symmetry. This differential approach allows us to solve the Yang–Baxter equation in a systematic way.

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“…is the trigonometric R-matrix associated with the quantum group [38] ( ( )) Û su n q , which was given in [39][40][41][42][43] and further studied in…”

Section: Su(n) Spin Torusmentioning

confidence: 99%

Exact solution of ansu(n) spin torus

Hao¹,

Cao²,

Li³

et al. 2016

J. Stat. Mech.

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The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix are derived. These identities and the asymptotic behavior of the transfer matrix together allow us to obtain the exact eigenvalues in terms of an inhomogeneous T − Q relation via the off-diagonal Bethe Ansatz.

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Characterization of completely X-symmetric factorized S-matrices for a special type of interaction applications to multicomponent field theories

Cited by 27 publications

References 8 publications

The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach

The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach

Solutions of the Yang–Baxter equation for (n + 1) (2n + 1)-vertex models using a differential approach

Exact solution of ansu(n) spin torus

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