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Some problems related to a completely antisymmetrized R-matrix theory

D. Baye, P.-H. Heenen

Jan 1, 19740 citations

New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions

Yao-Zhong Zhang, Jason L. Werry

Abstract We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra Uq(gl(2|1)), we obtain the explicit expression for the Uq(gl(2|1))− invariant R-matrix which is of non-difference form in spectral parameters. Using this R matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms.Abstract We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra Uq(gl(2|1)), we obtain the explicit expression for the Uq(gl(2|1))− invariant R-matrix which is of non-difference form in spectral parameters. Using this R matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms.

arXiv:2001.05096Journal of High Energy PhysicsMar 1, 20204 citations

Application of the Infinite Product Representation of the R-Matrix

Jinchu Huang

Jan 1, 19890 citations

Honeycomb lattice solvable models

Kwon, Kyung-Hoon, Doochul Kim

We construct solvable models on the honeycomb lattice by combining three faces of the square lattice solvable models into a hexagon face. These models contain two independent, anisotropy controlling, spectral parameters and their transfer matrices with different spectral parameters commute with each other. At the critical point, the finite-size scaling of the transfer matrix spectrum for the honeycomb lattice models is written in terms of the quantities obtained from the finite-size scaling of the square lattice solvable models. We study in detail the phase transition properties of two models based on the interacting hard square model and the magnetic hard square model, respectively. The models, in general, can be extended to the IRF version of the Z-invariant models of Baxter.We construct solvable models on the honeycomb lattice by combining three faces of the square lattice solvable models into a hexagon face. These models contain two independent, anisotropy controlling, spectral parameters and their transfer matrices with different spectral parameters commute with each other. At the critical point, the finite-size scaling of the transfer matrix spectrum for the honeycomb lattice models is written in terms of the quantities obtained from the finite-size scaling of the square lattice solvable models. We study in detail the phase transition properties of two models based on the interacting hard square model and the magnetic hard square model, respectively. The models, in general, can be extended to the IRF version of the Z-invariant models of Baxter.

arXiv:cond-mat/9303019Mar 10, 19930 citations

A nested sequence of projectors and corresponding braid matrices R(θ). 1. Odd dimensions

Amitabha Chakrabarti

A basis of N2 projectors, each an N2×N2 matrix with constant elements, is implemented to construct a class of braid matrices R̂(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors Pα appearing in the spectral decomposition of R̂(θ) leads to exponentials exp(mαθ) as the coefficient of Pα. The sums and differences of such exponentials on the diagonal and the antidiagonal, respectively, provide the (2N2−1) nonzero elements of R̂(θ). One element at the center is normalized to unity. A class of supplementary constraints imposed by the braid equation leaves 12(N+3)(N−1) free parameters mα. The diagonalizer of R̂(θ) is presented for all N. Transfer matrices t(θ) and L(θ) operators corresponding to our R̂(θ) are studied. Our diagonalizer signals specific combinations of the components of the operators that lead to a quadratic algebra of N2 constant N×N matrices. The θ dependence factors out for such combinations. R̂(θ) is developed in a power series in θ. The basic difference arising for even dimensions is made explicit. Some special features of our R̂(θ) are discussed in a concluding section.A basis of N2 projectors, each an N2×N2 matrix with constant elements, is implemented to construct a class of braid matrices R̂(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors Pα appearing in the spectral decomposition of R̂(θ) leads to exponentials exp(mαθ) as the coefficient of Pα. The sums and differences of such exponentials on the diagonal and the antidiagonal, respectively, provide the (2N2−1) nonzero elements of R̂(θ). One element at the center is normalized to unity. A class of supplementary constraints imposed by the braid equation leaves 12(N+3)(N−1) free parameters mα. The diagonalizer of R̂(θ) is presented for all N. Transfer matrices t(θ) and L(θ) operators corresponding to our R̂(θ) are studied. Our diagonalizer signals specific combinations of the components of the operators that lead to a quadratic algebra of N2 constant N×N matrices. The θ dependence factors out for such combinations. R̂(θ) is developed in a power series in θ. The basic difference arising for even dimensions is made explicit. Some special features of our R̂(θ) are discussed in a concluding section.

arXiv:math/0401207Journal of Mathematical PhysicsMay 23, 200513 citations

Standard r-Transformation Matrices and Their Applications

U. Fano, A. R. P. Rau

Elsevier eBooksJan 1, 19960 citations

A construction for R-matrices without difference property in the spectral parameter

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