The field of integrable systems is a vast one that has grown almost explosively in recent years. It is not remotely possible to review all the developments in the field in one hour, so I am restricting my attention to some particular topics. I shall only consider one dimensional quantum systems, or 1+1 as it is usually said, including the time dimension, but necessarily therefore including some...

We calculate exactly the entanglement content of magnon excited states in integrable spin-1/2 XXX and XXZ chains scaling limit. In particular, we show that as far number magnons with respect to size system is small one can decompose content, limit, sum particular free fermionic or bosonic theories. addition conjecture generic translational invariant Hamiltonians be also classified, operator Ham...

The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous dimension of single trace operators involving the three complex scalars of N = 4 supersymmetric Yang-Mills. We construct the non-linear sigma model describing the continuum limit of the SU(3) spin chain. We find that this sigma model corresponds to a string moving with large angular momentum in the five-sphere in AdS5...

We begin with a review of the antiferromagnetic spin 1/2 Heisenberg chain. In particular, we show that the model has particle-like excitations with spin 1/2, and we compute the exact bulk S matrix. We then review our recent work which generalizes these results. We first consider an integrable alternating spin 1/2 spin 1 chain. In addition to having excitations with spin 1/2, this model also has...

Analyses of databases derived from the Brookhaven Protein Data Bank have identified a set of related turn structures formed by the sequence Asx-Pro-Xxx(n). In a variety of flanking structural contexts, more than 60% of Asx-Pro sequences adopt a turn conformation stabilized by a set of alternative hydrogen bonds among the side chain O delta and backbone C = O carbonyl oxygens of Asx (residue i) ...

A bstract We consider the spectrum of anomalous dimensions in planar $$ \mathcal{N} N = 4 supersymmetric Yang-Mills theory and its 1 super-conformal Leigh-Strassler deformations. The two-loop truncation integrable dilatation operator SU(2) sector, which is a next-to-nearest-neighbour deformation XXX spin chai...

We examine dynamic quantities of a random spin-1/2 isotropic XY chain in a transverse field. The randomness is related to the sign of the nearest-neighbor exchange interaction and can be eliminated by a suitable transformation. As a result, the dynamic quantities for the random spin chain are related to the same dynamic quantities for the homogeneous spin chain. We use the available results for...

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that...