String Theory Journal Club

Analytical insights into interacting quantum many-body systems are hard to come by. A particularly difficult aspect to study is the precise characterization of the phase diagram of a system based on its entanglement properties. Recently, a version of this problem has been tackled in the context of holography via a novel take on an old paradigm, namely the theory of von Neumann algebras. Different types of algebras are known to encode distinct entanglement properties, and identifying their occurrence provides new perspectives into the different phases of a system. In this talk, I introduce a model of Majorana fermions with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. In particular, I study a four-site chain, which exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy. Based on these results, I identify transitions between types of von Neumann operator algebras throughout the phase diagram. In the strongly interacting limit, this transition occurs in correspondence with the quantum phase transition. This study provides a novel application of the theory of von Neumann algebras in the context of quantum many-body systems.