Nikos Karaiskos

Sigma models in the presence of dynamical point-like defects

Abstract Point-like Liouville integrable dynamical defects are introduced in the context of the Landau–Lifshitz and Principal Chiral (Faddeev–Reshetikhin) models. Based primarily on the underlying quadratic algebra we identify the first local integrals of motion, the associated Lax pairs as well as the relevant sewing conditions around the defect point. The involution of the integrals of motion is shown taking into account the sewing conditions.

Introduction to Quantum Integrability

In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary Yang-Baxter equations depending on the choice of boundary conditions. The relation between the aforementioned equations and the braid group is briefly discussed. A short review on quantum groups as well as the quantum inverse scattering method (algebraic Bethe ansatz) is also presented.

Transmission amplitudes from Bethe ansatz equations

A bstractWe consider the Heisenberg spin chain in the presence of integrable spin defects. Using the Bethe ansatz methodology, we extract the associated transmission amplitudes, that describe the interaction between the particle-like excitations displayed by the models and the spin impurity. In the attractive regime of the XXZ model, we also derive the breather’s transmission amplitude. We compare our findings with earlier relevant results in the context of the sine-Gordon model.

Brane embeddings in sphere submanifolds

Wrapping a D(8−p)-brane on AdS2 times a submanifold of S8 − p introduces point-like defects in the context of AdS/CFT correspondence for a Dp-brane background. We classify and work out the details in all possible cases with a single-embedding angular coordinate. Brane embeddings of the temperature and beta-deformed near-horizon D3-brane backgrounds are also examined. We demonstrate the relevance of our results to holographic lattices and dimers.

Bethe ansatz solution of the small polaron with nondiagonal boundary terms

The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The fusion hierarchy of the transfer matrices and its truncation for particular values of the anisotropy parameter are both employed, so that the spectral problem is formulated in terms of a TQ equation. The solution of this equation for generic boundary conditions is based on a deformation of the diagonal case. The eigenvalues of the model are extracted and the corresponding Bethe ansatz equations are presented. Finally, we comment on the eigenvectors of the model and explicitly compute the eigenstate of the model which evolves into the Fock vacuum when the off-diagonal boundary terms are switched off.

New reflection matrices for the Uq(gl(m|n)) case

We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U_q(gl(m|n)). The boundary super algebra is briefly discussed and it is shown to be central to the super symmetric realization of the B-type Hecke algebra

The

We consider the sl(N) twisted Yangian quantum spin chain. In particular, we study the bulk and boundary scattering of the model via the solution of the Bethe ansatz equations in the thermodynamic limit. Local defects are also implemented in the model and the associated transmission amplitudes are derived through the relevant Bethe ansatz equations.

\mathfrak{sl}({\mathcal N})

We consider the sl(N) twisted Yangian quantum spin chain. In particular, we study the bulk and boundary scattering of the model via the solution of the Bethe ansatz equations in the thermodynamic limit. Local defects are also implemented in the model and the associated transmission amplitudes are derived through the relevant Bethe ansatz equations.

twisted Yangian: bulk-boundary scattering and defects

A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explicitly determining the bulk and boundary scattering amplitudes. The energy and quantum numbers of the low lying excitations are also derived.A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected by the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explicitly determining the bulk and boundary scattering amplitudes. The energy and quantum numbers of the low lying excitations are also derived.

The sl(N) twisted Yangian: bulk-boundary scattering & defects

A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explicitly determining the bulk and boundary scattering amplitudes. The energy and quantum numbers of the low lying excitations are also derived.A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected by the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explicitly determining the bulk and boundary scattering amplitudes. The energy and quantum numbers of the low lying excitations are also derived.