0000000001225153

AUTHOR

Simone Faldella

showing 2 related works from this author

The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation

2012

The theory of classically integrable nonlinear wave equations, and the Bethe Ansatz systems describing massive quantum field theories defined on an infinite cylinder, are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper we shall describe this link for the case of the classical and quantum versions of the (Tzitz\'eica-)Bullough-Dodd model.

High Energy Physics - TheoryPhysicsQuantum PhysicsQuantum sigma modelsIntegrable system010308 nuclear & particles physicsGeneral MathematicsGeneral EngineeringGeneral Physics and AstronomyODE/IM correspondenceQuantum sigma models ODE/IM correspondence01 natural sciencesBethe ansatzNonlinear Sciences::Exactly Solvable and Integrable SystemsNonlinear wave equation0103 physical sciencesCylinderQuantum field theory010306 general physicsMathematical PhysicsMathematical physicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Solution of XXZ and XYZ spin chains with boundaries by separation of variables

2014

In this thesis we give accounts on the solution of the open XXZ and XYZ quantum spin-1/2 chains with the most generic integrable boundary terms. By using the the Separation of Variables method (SoV), due to Sklyanin, we are able, in the inhomogeneous case, to build the complete set of eigenstates and the associated eigenvalues. The characterization of these quantities is made through a maximal system of N quadratic equations, where N is the size of the chain. Different methods, like the Algebraic Bethe ansatz (ABA) or other generalized Bethe ansatz techniques, have been used, in the past, in order to tackle these problems. None of them resulted effective in the reproduction of the full set …

SpinXXZOpenXYZBoundaryChainsSeparation of variablesBethe[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]AnsatzSklyanin
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