Search results for "Algebraic Bethe ansatz"

showing 3 items of 3 documents

Partition function of the trigonometric SOS model with reflecting end

2010

We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.

Statistics and ProbabilityHigh Energy Physics - Theory[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]Domain wall boundary conditionsopen spin chainsFOS: Physical sciencesBoundary (topology)Type (model theory)01 natural sciences[ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th]Domain wall (string theory)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesASEPBoundary value problem010306 general physicsMathematical PhysicsMathematicsPartition function (quantum field theory)010308 nuclear & particles physics[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]Mathematical analysis[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Algebraic Bethe ansatzStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Square latticeReflection (mathematics)High Energy Physics - Theory (hep-th)[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]Statistics Probability and UncertaintyTrigonometry
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Asymptotic analysis of the form-factors of the quantum spin chains

2020

Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic, of the correlation function is one of the most important subject of the theory of the quantum integrable models. In this context an approach based on the calculation of form factors has been proved to be a more effective one. In this thesis, we develop a new method based on the algebraic Bethe ansatz is proposed for the computation of the form-factors in thermodynamic limit. It is applied to and described in the context of isotropic XXX Heisenberg chain, w…

Quantum inverse scattering methodFacteurs de formeXXX spin chainChaîne de spin XXXAlgebraic Bethe ansatzLimite thermodynamique[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Ansatz de Bethe algebriqueThermodynamic limitMéthode de la dispersion inverse[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Integrable systemsForm-FactorsSystèmes intégrables
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Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End

2011

In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid (SOS) model with one reflecting end and domain wall boundary conditions. We show that these two problems are related through a gauge transformation (so-called vertex-face transformation) and can be solved using the same dynamical reflection algebras.

High Energy Physics - TheorySOS modelsspin chainsDiagonalFOS: Physical sciencesBoundary (topology)algebraic Bethe ansatzMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)Boundary value problemGauge theoryMathematical PhysicsEigenvalues and eigenvectorsMathematicsSpin-½Partition function (statistical mechanics)Nonlinear Sciences - Exactly Solvable and Integrable Systemslcsh:MathematicsMathematical analysisMathematical Physics (math-ph)lcsh:QA1-939dynamical reflection algebraTransformation (function)High Energy Physics - Theory (hep-th)Geometry and TopologyExactly Solvable and Integrable Systems (nlin.SI)AnalysisSymmetry, Integrability and Geometry: Methods and Applications
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