In this talk I will review recent results co-authored with Stefano Negro, Fabio Sailis and István Szécsényi. In this project we have addressed the problem of how to compute correlation functions in integrable quantum field theories perturbed by irrelevant perturbations such as the operator TTbar. It has been known for some time that integrability is preserved under such perturbations even though the S-matrix is modified by a CDD factor. Therefore, it is natural to expect that matrix elements of local fields may be computed by employing the standard form factor program, which was developed for integrable quantum field theories in the 70s. By doing so we have found that the form factors of local and semi-local fields have a universal structure which we have identified. This gives rise to correlation functions with distinct convergence/divergence properties, depending on the sign of the perturbation. In the convergent regime we find that the correlation functions scale as power-laws at short distances, similar to standard integrable quantum field theories, but with powers that are no longer the conformal dimensions of some field. At the heart of our construction is a function called the minimal form factor, whose structure I will discuss in some detail.

This is the live session included as part of the LonTI lecture on Entanglement in 1+1D Quantum Field Theory. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. In this short course I will introduce branch point twist fields and explain how they emerge in the context of computing entanglement measures in 1+1D. I will focus on massive 1+1D integrable quantum field theory (IQFT) and also comment on some well-known results in conformal field theory (CFT). The talk will be structured into three main parts: First, I will introduce entanglement measures, focussing on the entanglement entropy, explain how these measures relate to partition functions in multi-sheeted Riemann surfaces and how these, in turn, may be expressed as correlators of branch point twist fields. Second, I will show how several well-known results in CFT and IQFT are very easily derived in this branch point twist field picture and how they can also be recovered numerically in a quantum spin chain. Finally, I will explain how more involved computations with branch point twist fields may be performed by exploiting form factor technology and will end the talk by showing an example of one such calculation.

This tutorial is available via youtube at https://youtu.be/zU-BRF6xLik. In this short course I will introduce branch point twist fields and explain how they emerge in the context of computing entanglement measures in 1+1D. I will focus on massive 1+1D integrable quantum field theory (IQFT) and also comment on some well-known results in conformal field theory (CFT). The talk will be structured into three main parts: First, I will introduce entanglement measures, focussing on the entanglement entropy, explain how these measures relate to partition functions in multi-sheeted Riemann surfaces and how these, in turn, may be expressed as correlators of branch point twist fields. Second, I will show how several well-known results in CFT and IQFT are very easily derived in this branch point twist field picture and how they can also be recovered numerically in a quantum spin chain. Finally, I will explain how more involved computations with branch point twist fields may be performed by exploiting form factor technology and will end the talk by showing an example of one such calculation.

n this talk I will review the results of recent work in collaboration with Cecilia De Fazio, Benjamin Doyon and István M. Szécsényi. We studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state in a simple bi-partition of a quantum system, where both the size of the system and of the bi-partition are infinite, but their ratio is finite. We originally studied this problem in massive 1+1 dimensional QFTs where analytic computations were possible. We have found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localised in one or the other part of the bi-partition. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and present some numerical data.

In this talk I will review some of the main results of my research in this area, which stated in 2007 in collaboration with John L. Cardy and Benjamin Doyon. I will emphasise how a special type of field we have named branch point twist field has become an essential tool for performing computations of the entanglement entropy in non-critical systems. I will show how the relationship between correlators of twist fields and entanglement entropy allows us to recover well-known results for critical systems but also to predict new results for theories with a finite correlation length. Time permitting, I will mention some more recent results extending our understanding to non-unitary critical and non-critical systems.

The homogeneous and symmetric space sine-Gordon models (HSG- and SSSG-models, for short) are two groups of two-dimensional integrable quantum field theories which belong to a larger class of models: the non-Abelian affine Toda field theories. In this talk I intend to review the main results known up to date about these two classes of models, paying special attention to my own contributions to the subject. These contributions have focused on the one hand, on the development of the bootstrap program for the HSG-models (TBA-analysis, computation of form factors and correlation functions etc) and, on the other hand, on the study of the quantum integrability and spectrum of a subset of the SSSG-models, known as split models.

In this talk I will present a short review on the algebraic Bethe ansatz technique and on the recently found solution of the so-called inverse problem. I will show how this solution provides a means for the explicit and exact computation of correlation functions in spin chains and summarize some of the many results obtained in this direction by members of the theory group at the ENS-Lyon in the last years. Finally I will present some work still in progress which intends the generalization of these techniques to the case of spin chains in the presence of impurities.