New Frontiers on Entanglement Measures in the Quantum sine-Gordon Model

Branch Point Twist Fields are a leading tool in the context of the analytic computation of entanglement measures in 1+1D quantum field theory (QFT). Their usefulness follows from the relationship between entanglement measures and correlation functions of branch point twist fields. More precisely, in 1+1D entanglement measures can be expressed in terms of n-point functions of branch point twists fields, where n is the number of boundary points between the regions A and B whose mutual bipartite entanglement is being evaluated. Since this approach was introduced for massive theories in 2007, branch point twist fields have been employed in multiple contexts to either study features of entanglement (both at and away from equilibrium) or to construct building blocks of generic entanglement measures (i.e. form factors). The PI has been involved in much of this work.

Despite substantial activity, integrable QFTs with non-diagonal scattering have been much less studied due to the well-known complexities of form factor computations. In particular, for the most paradigmatic non-diagonal integrable QFT, the sine-Gordon model, there have been only two publications in recent years, both involving the PI. The first in 2009 was a study of the repulsive regime of the theory (where the particle spectrum is particularly simple), and more recently, in the current year, a more ambitious study for the full range of values of the coupling (hence a much more involved particle spectrum) was carried out. This recent work was in collaboration with David X. Horvath (SISSA, Italy).

The current proposal follows organically from this recent collaboration which has created an opportunity for a much more ambitious study of the problem. In particular, our joint expertise, puts us in the best position to consider one of the most recent entanglement measures of interest, namely the symmetry resolved entanglement entropy, in the sine-Gordon model. It has been recently discovered that in the presence of an internal symmetry, the structure of the reduced density matrix in terms of which all entanglement measures are constructed, is highly predictable and regular. In general, it is block-diagonal, which block-sizes relating to the underlying symmetry. This also means that each block makes a contribution to entanglement measures and that those individual contributions can be computed as quantities of particular interest. Following this observation, Horváth and Calabrese (2020) have developed a new form factor programme for a generalized branch point twist field whose correlators give the block contributions to entanglement.

One of the main objectives of this project is to compute the form factors of these new branch point twist fields in the sine-Gordon model, study their analytical properties, hence the analytical properties of the symmetry resolved entanglement. This project requires advanced knowledge of the technicalities involved in such types of computation, which the PI and collaborators have an excellent track record of.