Related papers: Integrable crosscaps in classical sigma models

Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…

We present a statistical analysis of spectra of transfer matrices of classical lattice spin models; this continues the work on the eight-vertex model of the preceding paper. We show that the statistical properties of these spectra can serve…

We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…

The notion of a crosscap state, a special conformal boundary state first defined in 2d CFT, was recently generalized to 2d massive integrable quantum field theories and integrable spin chains. It has been shown that the crosscap states…

We consider integrable boundary states in the XXX spin-1/2 spin chain. We begin by briefly reviewing the algebraic Bethe Ansatz as well as integrable boundary states in spin chains. Then a recently discovered class of integrable states…

The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature…

We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…

We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin…

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…

The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…

We consider the case of an integrable quantum spin chain with ``soliton non-preserving'' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…

The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a…

A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality…

The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…

We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the…

The purpose of this talk is to address a couple of simple-sounding questions: what boundary conditions are compatible with (a) Classical integrability? (b) Quantum integrability?

In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…

In this contribution we briefly review recent developments in the theory of long-range integrable spin chains. These spin chains constitute a natural generalisation of the well-studied integrable nearest-neighbour chains and are of…

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of…