0000000000441657

AUTHOR

Giuliano Niccoli

showing 3 related works from this author

Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

2014

28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…

Statistics and ProbabilityPhysicsIntegrable system010308 nuclear & particles physics[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th][PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]Finite differenceSeparation of variablesStatistical and Nonlinear Physics01 natural sciencesTransfer matrixBethe ansatzsymbols.namesake0103 physical sciencessymbols[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Boundary value problemStatistics Probability and Uncertainty010306 general physicsHamiltonian (quantum mechanics)QuantumMathematical physics
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SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra

2013

The analysis of the transfer matrices associated to the most general representations of the 8-vertex reflection algebra on spin-1/2 chains is here implemented by introducing a quantum separation of variables (SOV) method which generalizes to these integrable quantum models the method first introduced by Sklyanin. More in detail, for the representations reproducing in their homogeneous limits the open XYZ spin-1/2 quantum chains with the most general integrable boundary conditions, we explicitly construct representations of the 8-vertex reflection algebras for which the transfer matrix spectral problem is separated. Then, in these SOV representations we get the complete characterization of t…

High Energy Physics - TheoryStatistics and ProbabilityNonlinear Sciences - Exactly Solvable and Integrable SystemsIntegrable systemSpectrum (functional analysis)General Physics and AstronomyFOS: Physical sciencesStatistical and Nonlinear PhysicsBasis (universal algebra)Mathematical Physics (math-ph)16. Peace & justiceTransfer matrixAlgebraMatrix (mathematics)Reflection (mathematics)High Energy Physics - Theory (hep-th)Modeling and SimulationAlgebra representationExactly Solvable and Integrable Systems (nlin.SI)Mathematical PhysicsEigenvalues and eigenvectorsMathematics
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Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms

2013

We use the quantum separation of variable (SOV) method to construct the eigenstates of the open XXZ chain with the most general boundary terms. The eigenstates in the inhomogeneous case are constructed in terms of solutions of a system of quadratic equations. This SOV representation permits us to compute scalar products and can be used to calculate form factors and correlation functions.

Statistics and ProbabilityPhysicsHigh Energy Physics - TheoryStatistical Mechanics (cond-mat.stat-mech)Nonlinear Sciences - Exactly Solvable and Integrable Systems010308 nuclear & particles physicsDiagonalScalar (mathematics)Separation of variablesFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)01 natural sciencesQuadratic equationNonlinear Sciences::Exactly Solvable and Integrable SystemsHigh Energy Physics - Theory (hep-th)0103 physical sciencesExactly Solvable and Integrable Systems (nlin.SI)Statistics Probability and Uncertainty010306 general physicsQuantumEigenvalues and eigenvectorsMathematical PhysicsCondensed Matter - Statistical MechanicsMathematical physics
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