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E. Ragoucy

Publications and source records attributed to E. Ragoucy.

At least 73 records · Page 4Linked to original sources
arXiv2014

Coordinate Bethe Ansätze for non-diagonal boundaries

Talk given at "Quantum Integrable Systems and Geometry" (3-7 September 2012, Olhao, Portugal) and based on joint works with S. Belliard, N. Crampe and D. Simon, see arXiv:1009.4119, arXiv:1105.4119, arXiv:1106.3264 and arXiv:1209.4269. This short note presents only the basic ideas of the technique, and does not attend to give a general overview of the subject. Interested readers should refer to the original papers and references therein.

math-ph↗
arXiv2013

Scalar products in models with GL(3) trigonometric R-matrix. Highest coefficient

We study quantum integrable models with GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of the highest coefficients. We show that in the models with GL(3) trigonometric R-matrix there exist two different highest coefficients. We obtain various representations for them in terms of sums over partitions. We also prove several important properties of the highest coefficients, which are necessary for the evaluation of the scalar products.

math-ph↗
arXiv2013

Bethe vectors of quantum integrable models based on Uq(gl(N))

We study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by certain morphisms of the positive Borel subalgebra in Uq(gl(N)) into analogous subalgebra in Uq'(gl(N)), with q'=1/q.

math-ph↗
arXiv2013

Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz

We classify all Hamiltonians with rank 1 symmetry, acting on a periodic three-state spin chain, and solvable through (generalisation of) the coordinate Bethe ansatz (CBA). We obtain in this way four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin, Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exists 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonian, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We get also two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. A special attention is made to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

math-ph↗
arXiv2013

Yangians and W-algebras

We present a connection between W-algebras and Yangians, in the case of gl(N) algebras, as well as for twisted Yangians and/or super-Yangians. This connection allows to construct an R-matrix for the W-algebras, and to classify their finite-dimensional irreducible representations. We illustrate it in the framework of nonlinear Schroedinger equation in 1+1 dimension.

math-ph↗
arXiv2013

Form factors in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.

math-ph↗
arXiv2013

Bethe vectors of GL(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian Y(sl(3)) on Bethe vectors are considered. These actions are relevant for the calculation of correlation functions and form factors of local operators of the underlying quantum models.

math-ph↗
arXiv2013

Algebraic Bethe ansatz for open XXX model with triangular boundary matrices

We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic Bethe ansatz. As usual, the method also provides Bethe equations and transfer matrix eigenvalues.

math-ph↗
arXiv2013

Superstring amplitudes and the associator

We investigate a pattern in the $α'$ expansion of tree-level open superstring amplitudes which correlates the appearance of higher depth multiple zeta values with that of simple zeta values in a particular way. We rephrase this relationship in terms of the coaction on motivic multiple zeta values and show that the pattern takes a very simple form, which can be simply explained by relating the amplitudes to the Drinfel'd associator derived from the Knizhnik-Zamolodchikov equation. Given this correspondence we show that, at least in the simplest case of the four-point amplitude, the associator can be used to extract the form of the amplitude.

hep-th↗
arXiv2012

Highest coefficient of scalar products in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.

math-ph↗
arXiv2012

Casimir elements from the Brauer-Schur-Weyl duality

We consider Casimir elements for the orthogonal and symplectic Lie algebras constructed with the use of the Brauer algebra. We calculate the images of these elements under the Harish-Chandra isomorphism and thus show that they (together with the Pfaffian-type element in the even orthogonal case) are algebraically independent generators of the centers of the corresponding universal enveloping algebras.

math.RT↗
arXiv2012

Generalized coordinate Bethe ansatz for non diagonal boundaries

We compute the spectrum and the eigenstates of the open XXX model with non-diagonal (triangular) boundary matrices. Since the boundary matrices are not diagonal, the usual coordinate Bethe ansatz does not work anymore, and we use a generalization of it to solve the problem.

hep-th↗
arXiv2011

Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries

We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.

hep-th↗
arXiv2011

Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models

We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This "matrix coordinate Bethe Ansatz" can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in

cond-mat.stat-mech↗
arXiv2011

Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions

In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.

math-ph↗
arXiv2010

Yangian symmetry of light-like Wilson loops

We show that a certain class of light-like Wilson loops exhibits a Yangian symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills theory in a certain kinematical regime. The fact that we find a Yangian symmetry constraining their functional form can be thought of as the effect of the original conformal symmetry associated to the scattering amplitudes in the N=4 theory.

hep-th↗
arXiv2010

Including a phase in the Bethe equations of the Hubbard model

We compute the Bethe equations of generalized Hubbard models, and study their thermodynamical limit. We argue how they can be connected to the ones found in the context of AdS/CFT correspondence, in particular with the so-called dressing phase problem. We also show how the models can be interpreted, in condensed matter physics, as integrable multi-leg Hubbard models.

hep-th↗