Baxter operators for the noncompact quantum<i>sl</i>(3) invariant spin chain

Derkachov, S. E.; Manashov, A. N.

doi:10.1088/0305-4470/39/42/001

Cited by 10 publications

(21 citation statements)

References 25 publications

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“…For generic values of the spins ℓ 1 , ℓ 2 the operatorsŘ (i) [16,18,19] act within the tensor product of the corresponding representation spaces, whereas the operators S i map to tensor products with changed spin values. Moreover, in the case of finite dimensional representations only the R-matrix itself leaves the tensor product space invariant.…”

Section: 2)mentioning

confidence: 99%

Yang–Baxter -operators and parameter permutations

2007

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We present an uniform construction of the solution to the Yang-Baxter equation with the symmetry algebra sℓ(2) and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the tensor product of two representations of the symmetry algebra with arbitrary spins ℓ 1 and ℓ 2 is built in terms of products of three basic operators S 1 , S 2 , S 3 which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group S 4 , the permutation group of the four parameters entering the RLL-relation.1

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Section: 2)mentioning

confidence: 99%

Yang–Baxter -operators and parameter permutations

2007

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“…Making use of the automorphism of the SL(2|1) superalgebra (2.9), one can obtain from (2.21) the decomposition of the 22) where [j] − denotes the antichiral SL(2|1) representation. It is spanned by the statesΦ(z, θ,θ) ∈ Vj which verify the conditionDΦ = 0.…”

Section: θmentioning

confidence: 99%

“…(3.6), a general infinite-dimensional transfer matrix (3.18) can be factorized into the product of the three operators (3.20). Calculation goes along the same lines as for the SL(3) spin chain [22] and details can be found in Appendix E. The resulting factorized expression for the transfer matrix reads 23) with the spectral parameters w 1 = w − j + j q , w 2 = w − j +j + j q −j q and w 3 = w +j −j q . In Eq.…”

Section: Definition Of Q−operatorsmentioning

confidence: 99%

“…Another remarkable feature of the Baxter operators is that the Hamiltonian of the SL(2) spin chain can be expressed in terms of the 'polynomial' Q−operator as H SL(2) = (ln Q + (s)) ′ − (ln Q + (−s)) ′ , (1.9) where the prime denotes a derivative with respect to the spectral parameter. For the SL(3) invariant homogeneous spin chain, one already encounters three Q−operators [20,21,22]. Similarly to (1.7), three Q−operators satisfy the same TQ-relation.…”

Section: Introductionmentioning

confidence: 99%

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The BaxterQ-operator for the gradedSL(2|1) spin chain

Belitsky¹,

Derkachov²,

Korchemsky³

et al. 2007

J. Stat. Mech.

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We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N = 1 super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the quantum space in all sites corresponding to infinite-dimensional representations of the SL(2|1) group. We extend the method of the Baxter Q−operator to spin chains with supergroup symmetry and apply it to determine the eigenspectrum of the model. Our analysis relies on a factorization property of the R−operators acting on the tensor product of two generic infinite-dimensional SL(2|1) representations. It allows us to factorize an arbitrary transfer matrix into a product of three 'elementary' transfer matrices which we identify as Baxter Q−operators. We establish functional relations between transfer matrices and use them to derive the TQ-relations for the Q−operators. The proposed construction can be generalized to integrable models based on supergroups of higher rank and, in distinction to the Bethe Ansatz, it is not sensitive to the existence of the pseudovacuum state in the quantum space of the model.

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“…For conventional (infinite-dimensional) sl(N ) magnets the property (4.10) does not hold (see [34,37,38]). Another property of the Baxter operators which we want to mention is related to the factorization property of the transfer matrix.…”

Section: The Operators R (K)mentioning

confidence: 99%