It was noticed many years ago, in the framework of massless RG flows, that the irrelevant composite operator TT, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum field theories, and can be regarded as a peculiar kind of integrable perturbation. Novel interesting features of this operator have recently emerged from the study of effective string theory models.In this paper we study further properties of this distinguished perturbation. We discuss how it affects the energy levels and one-point functions of a general 2D QFT in finite volume through a surprising relation with a simple hydrodynamic equation. In the case of the perturbation of CFTs, adapting a result by Lüscher and Weisz we give a compact expression for the partition function on a finite-length cylinder and make a connection with the exact g-function method. We argue that, at the classical level, the deformation naturally maps the action of N massless free bosons into the Nambu-Goto action in static gauge, in N + 2 target space dimensions, and we briefly discuss a possible interpretation of this result in the context of effective string models.

We evaluate the entanglement entropy of a single connected region in excited states of onedimensional massive free theories with finite numbers of particles, in the limit of large volume and region length. For this purpose, we use finite-volume form factor expansions of branch-point twist field two-point functions. We find that the additive contribution to the entanglement due to the presence of particles has a simple "qubit" interpretation, and is largely independent of momenta: it only depends on the numbers of groups of particles with equal momenta. We conjecture that at large momenta, the same result holds for any volume and region lengths, including at small scales. We provide accurate numerical verifications.

We investigate the quantum entanglement content of quasi-particle excitations in extended manybody systems. We show that such excitations give an additive contribution to the bi-partite von Neumann and Rényi entanglement entropies that takes a simple, universal form. It is largely independent of the momenta and masses of the excitations, and of the geometry, dimension and connectedness of the entanglement region. The result has a natural quantum information theoretic interpretation as the entanglement of a state where each quasi-particle is associated with two qubits representing their presence within and without the entanglement region, taking into account quantum (in)distinguishability. This applies to any excited state composed of finite numbers of quasi-particles with finite De Broglie wavelengths or finite intrinsic correlation length. We derive this result analytically in one-dimensional massive bosonic and fermionic free field theories and for simple setups in higher dimensions. We provide numerical evidence for the harmonic chain and the two-dimensional harmonic lattice in all regimes where excitations have quasi-particle properties. Finally, we provide supporting calculations for integrable spin chain models and other situations without particle production. Our results point to new possibilities for creating entangled states using many-body quantum systems. arXiv:1805.04948v1 [cond-mat.stat-mech]

We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series. -mails: diegobombardelli@gmail.com, alessandra.cagnazzo@desy.de, rouven.frassek@durham.ac.uk, fedor.levkovich@gmail.com, loebbert@physik.hu-berlin.de, stefano.negro@lpt.ens.fr, sfondria@itp.phys.ethz.ch, i.m.szecsenyi@durham.ac.uk, svantongeren@physik.hu-berlin.de, a.torrielli@surrey.ac.uk arXiv:1606.02945v2 [hep-th] Jul 2016In this article we introduce a series of articles reviewing aspects of integrable models. The articles provide a pedagogical introduction to the topic of integrability, with special emphasis on methods relevant in the AdS/CFT correspondence. After a brief motivation regarding the value of general integrable models in the development of theoretical physics, here we discuss the application of the framework of integrability to the AdS/CFT correspondence.We then provide an overview of the material contained in the various reviews, referring back to AdS/CFT applications, and indicating links between the reviews themselves and to the relevant literature. While written with an AdS/CFT background in mind, the methods covered in the reviews themselves have applications throughout the wider field of integrability. IntegrabilityIntegrable models appear throughout theoretical physics, starting from classical mechanics where models such as the Kepler problem can be solved-in the sense of the Liouville theorem-by integration. In general, integrable models show special behaviour due to many underlying symmetries, symmetries due to which they can often be exactly solved. Only a fraction of the physical systems appearing in nature can be described in these terms. Nevertheless, integrable models offer insight into real-world situations through universality, or when used as a theoretical laboratory to develop new ideas. In statistical mechanics for example, many subtleties of the thermodynamic limit have been understood by working out specific models, notably phase transitions in the Lenz-Ising model and the role of boundary conditions in the ice model. In hydrodynamics, the Korteweg-de Vries equation illustrates how a nonlinear partial differential equation can admit stable, wave-like localized solutions: solitons. In condensed matter physics, both integrable quantum spin chains and one-dimensional gases of almost-free particles play a pivotal role. Finally, in quantum field theories (QFTs) in two space-time dimensions, exactly solvable models helped unravel phenomena like dimensional transmutation, as in the case of the chiral Gross-Neveu model, or concepts like bosonisation, as in the case of the sine-Go...

In this paper we study the increment of the entanglement entropy and of the (replica) logarithmic negativity in a zero-density excited state of a free massive bosonic theory, compared to the ground state. This extends the work of two previous publications by the same authors. We consider the case of two disconnected regions and find that the change in the entanglement entropy depends only on the combined size of the regions and is independent of their connectivity. We subsequently generalize this result to any number of disconnected regions. For the replica negativity we find that its increment is a polynomial with integer coefficients depending only on the sizes of the two regions. The logarithmic negativity turns out to have a more complicated functional structure than its replica version, typically involving roots of polynomials on the sizes of the regions. We obtain our results by two methods already employed in previous work: from a qubit picture and by computing four-point functions of branch point twist fields in finite volume. We test our results against numerical simulations on a harmonic chain and find excellent agreement.