New $D_{n+1}^{(2)}$ K-matrices with quantum group symmetry

Nepomechie, Rafael I.; Pimenta, Rodrigo A.

doi:10.1088/1751-8121/aad957

Cited by 12 publications

(43 citation statements)

References 25 publications

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“…where R 12 = R ⊗ I, R 23 = I ⊗ R and R 13 = P 12 R 23 P 12 ; moreover, I is the identity matrix and P is the permutation matrix. We consider here the trigonometric R-matrices given by Jimbo [6] (except for A (2) 2n−1 , in which case we consider instead Kuniba's R-matrix [7]), corresponding to the following non-exceptional affine Lie algebras 1 g = A (2) 2n−1 , A (2) 2n , B (1) n , C (1) n , D (1) n , D…”

Section: R-matrixmentioning

confidence: 99%

“…We use the specific expressions for the R-matrices given in Appendix A of [1] and (for D (2) n+1 ) Appendix A of [21], where the anisotropy parameter is denoted by η. We emphasize that, as in [1,2], we consider here exclusively generic values of η. Various useful parameters related to these R-matrices are collected in Table 1.…”

Section: R-matrixmentioning

confidence: 99%

“…and (2.4) respectively. The crossing parameter ρ is given in Table 1, and the matrix M can be found in [1] and (for D (2) n+1 ) [21]. For all the cases except D (2) n+1 , we take for the right K-matrices the following d×d diagonal matrices [9,11,12,13] K R (u, p) = diag e −u , .…”

Section: K-matricesmentioning

confidence: 99%

“…Several infinite families of integrable open quantum spin chains with quantum group (QG) symmetry have recently been identified [1,2]. The transfer matrices for these models are constructed [3] from trigonometric R-matrices, which are associated to non-exceptional affine Lie algebrasĝ [4,5,6,7], and from certain K-matrices (also known as reflection matrices, or boundary S-matrices) depending on a discrete parameter p [8,9,10,11,12,13,2]. These transfer matrices have QG symmetry corresponding to removing the p th node from theĝ Dynkin diagram, as summarized in Tables 2 and 3.…”

Section: Introductionmentioning

confidence: 99%

“…The outline of this paper is as follows. The construction of the transfer matrix and key results from [1,2] are briefly reviewed in Sec. 2.…”

Section: Introductionmentioning

confidence: 99%

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The spectrum of quantum-group-invariant transfer matrices

Nepomechie

Retore

2019

Nuclear Physics B

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Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebrasĝ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the p th node from theĝ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type.We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.

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Section: R-matrixmentioning

confidence: 99%

Section: R-matrixmentioning

confidence: 99%

Section: K-matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The outline of this paper is as follows. The construction of the transfer matrix and key results from [1,2] are briefly reviewed in Sec. 2.…”

Section: Introductionmentioning

confidence: 99%

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The spectrum of quantum-group-invariant transfer matrices

Nepomechie

Retore

2019

Nuclear Physics B

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Finite size spectrum of the staggered six-vertex model with Uq($$ \mathfrak{sl} $$(2))-invariant boundary conditions

Frahm

Gehrmann

2022

J. High Energ. Phys.

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The finite size spectrum of the critical ℤ2-staggered spin-1/2 XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact SU(2, ℝ)/U(1) Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model.

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Lattice regularisation of a non-compact boundary conformal field theory

Robertson

Jacobsen

Saleur

2021

J. High Energ. Phys.

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Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of lattice models with a finite number of degrees of freedom per site. However, results have so far been restricted to the case of periodic boundary conditions, precluding the exploration via lattice models of aspects of non-compact boundary CFTs and the corresponding D-brane constructions.The present paper follows a series of previous works on a ℤ2-staggered XXZ spin chain, whose continuum limit is known to be a non-compact CFT related with the Euclidian black hole sigma model. By using the relationship of this spin chain with an integrable $$ {D}_2^2 $$ D 2 2 vertex model, we here identify integrable boundary conditions that lead to a continuous spectrum of boundary exponents, and thus correspond to non-compact branes. In the context of the Potts model on a square lattice, they correspond to wired boundary conditions at the physical antiferromagnetic critical point. The relations with the boundary parafermion theories are discussed as well. We are also able to identify a boundary renormalisation group flow from the non-compact boundary conditions to the previously studied compact ones.

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New $D_{n+1}^{(2)}$ K-matrices with quantum group symmetry

Cited by 12 publications

References 25 publications

The spectrum of quantum-group-invariant transfer matrices

The spectrum of quantum-group-invariant transfer matrices

Finite size spectrum of the staggered six-vertex model with Uq($$ \mathfrak{sl} $$(2))-invariant boundary conditions

Lattice regularisation of a non-compact boundary conformal field theory

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