Adrián Franco-Rubio

Postdoctoral Researcher at the Max Planck Institute for Quantum Optics

Research interests

My main research interests include quantum many-body and information theory, condensed matter physics, mathematical physics and quantum field theory.

My current research belongs to the area of tensor networks, a set of mathematical constructions introduced as computational tools to improve the efficiency of numerical simulations in quantum many-body physics, which have also proven themselves capable of providing new theoretical insights into the properties of quantum many-body states. I am interested in results on the approximability of said states via tensor networks, and in extracting information (e.g. topological properties) of the corresponding quantum phases from their tensor network representation.

I have also worked extensively in the area of continuous tensor networks, the quantum field theoretic version of tensor networks. There, I have been looking into ways of implementing renormalization group (RG) transformations. The renormalization group provides a way to study a physical system scale by scale, connecting the microphysics operating at small distances with the macrophysics observed at long distances, and it has proven of great importance to understand both quantum field theory and condensed matter theory.

Intimately related to RG are those theories that are left invariant under RG flow: these fixed-point theories are conformal field theories (CFTs), and they are key to understanding phase transitions and critical phenomena. Part of my recent work has focused on investigating the influence of the symmetries of the underlying conformal field theory on lattice systems at criticality.

In the past I did some work on a different kind of tensor networks called holographic quantum error correcting codes. They provide an example of an exciting exchange of ideas between quantum many-body theory / quantum information theory and the subject of holography, which is motivating increased efforts in bridging the two fields of study.

I am also quite fond of abstract thinking and have a taste for purely mathematical problems, as well as for applications in physics of beautiful mathematical formalisms. My first steps in physics research where given within the context of geometrical quantum mechanics, where the language of differential geometry can be used to study and interpret quantum phenomena such as decoherence. Recently I have been enjoying learning about quantum symmetries, operator algebras and subfactor theory, which together display deep connections to conformal field theory and condensed matter theory.