After two years, most of our effort has been dedicated to building a coherent group of researchers, and train them in the intricacies of tensor networks and their continuum version. Indeed, it is a fairly new subject that only a handful of people know in the world.
Now with a strong and balanced team we have started working on most parts of the project, and in particular the extension of the method to new models of quantum field theories, so far exclusively in low dimension.
More precisely, we have worked on extending the continuous tensor network technology to two new models 1) one with symmetries, the so called complex scalar field 2) one with interactions similar to that of electromagnetism, the Schwinger model. This work is still in progress, but in particular for the first model, we expect concrete results next year.
Our effort has also revolved around the calculation of new quantities in quantum field theory, that are not trivial to access with other techniques. We have written a preprint on the inclusion of so called ""defect operators"", which are an important new class of observables, and are currently working on estimating spectral data, an example of which is the mass of fundamental particles.
Finally, we had to take into account new developments in the field during the project, the most important being the hybridization of tensor networks with semi-definite programming. We strongly believe that most parts of the project could benefit from this new technique. To grow our own expertise on it, we applied it to a simple example outside of quantum field theory. We obtained unexpectedly interesting results that are written in a preprint. We hope that it will soon be formally accepted in a journal.
