Anastasia Doikou

Bulk and boundary S-matrices for the SU(N) chain

Abstract We consider both closed and open integrable antiferromagnetic chains constructed with the SU ( N )-invariant R -matrix. For the closed chain, we extend the analyses of Sutherland and Kulish — Reshetikhin by considering also complex “string” solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU ( N ) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [ k ] of SU ( N ), with k = 1, …, N − 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [ N − 1 ]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU ( l ) × SU ( N − l ) × U (1), as well as a new “duality” symmetry which maps l → N − l . With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [ N − 1 ] the corresponding boundary S-matrices.

The sine-Gordon model with integrable defects revisited

A bstractApplication of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.

Liouville integrable defects: the non-linear Schrödinger paradigm

A bstractA systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrödinger model in the presence of a single particle-like defect is investigated through this algebraic approach. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. Coincidence of our results with the continuum limit of the discrete expressions obtained in earlier works further confirms our approach.

DUALITY AND QUANTUM-ALGEBRA SYMMETRY OF THE AN-1(1) OPEN SPIN CHAIN WITH DIAGONAL BOUNDARY FIELDS

We show that the transfer matrix of the AN−1(1) open spin chair with diagonal boundary fields has the symmetry Uq(SU(l)) × Uq(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.

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.

Defects in the discrete non-linear Schrödinger model

Abstract The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.

On reflection algebras and twisted Yangians

It is well known that integrable models associated to rational R matrices give rise to certain non-Abelian symmetries known as Yangians. Analogously boundary symmetries arise when general but still integrable boundary conditions are implemented, as originally argued by Delius, Mackay, and Short from the field theory point of view, in the context of the principal chiral model on the half-line. In the present study we deal with a discrete quantum mechanical system with boundaries, that is the N site gl(n) open quantum spin chain. In particular, the open spin chain with two distinct types of boundary condition known as soliton preserving and soliton nonpreserving is considered. For both types of boundaries we present a unified framework for deriving the corresponding boundary nonlocal charges directly at the quantum level. The nonlocal charges are simply coproduct realizations of particular boundary quantum algebras called boundary or twisted Yangians, depending on the choice of boundary conditions. Finally,...

Fused integrable lattice models with quantum impurities and open boundaries

The alternating integrable spin chain and the RSOS(q1,q2;p) model in the presence of a quantum impurity are investigated. The boundary free energy due to the impurity is derived, the ratios of the corresponding g functions at low and high temperature are specified and their relevance to boundary flows in unitary minimal and generalized coset models is discussed. Finally, the alternating spin chain with diagonal and non-diagonal integrable boundaries is studied, and the corresponding boundary free energy and g functions are derived.

Boundary non-local charges from the open spin chain

The N site open XXZ quantum spin chain with a right non-diagonal boundary and special diagonal left boundary is considered. The boundary non-local charges originally obtained from a field theoretical viewpoint, for the sine–Gordon model on the half line, are recovered from the spin chain point of view. Furthermore, the symmetry of the open spin chain is exhibited. More specifically, we show that certain non-local charges commute with the transfer matrix of the open spin chain, depending on the choice of boundary conditions. In addition, we show explicitly that for a special choice of the left boundary one of the non-local charges, in a particular representation, commutes with each one of the generators of the blob algebra, and hence with the corresponding local Hamiltonian.

Boundary Lax pairs for the An(1) Toda field theories

Abstract Based on the recent formulation of a general scheme to construct boundary Lax pairs, we develop this systematic construction for the A n ( 1 ) affine Toda field theories (ATFT). We work out explicitly the first two models of the hierarchy, i.e. the sine-Gordon ( A 1 ( 1 ) ) and the A 2 ( 1 ) models. The A 2 ( 1 ) Toda theory is the first non-trivial example of the hierarchy that exhibits two distinct types of boundary conditions. We provide here novel expressions of boundary Lax pairs associated to both types of boundary conditions.