Research Projects

Many body quantum systems with restricted geometries appear in different physical systems, such as Ising model bounded by intersecting planes. Such deformed geometry leads to partial breaking of translational invariance which makes it challenging to predict the dynamics in a controllable way. These systems are described by conformal field theories (CFTs) with intersecting boundaries that capture the corner and edge effects at criticality. This setup is known as wedge CFT (WCFT). In addition to bulk observables, the wedge-shaped geometry gives rise to new set of observables localised on the edge or surface. The dynamics of WCFT is captured by the spectrum and expansion coefficients of local operators, known as wedge CFT data. The interplay between bulk, surface and edge observables makes the structure richer than the usual CFT without boundaries or edges. The WCFT data can be computed by probing the correlation functions of local operators. This area of research is largely unexplored and general results related to edge observables are missing. The renormalisation group (RG) flow from one CFT to another in presence of bulk, surface or edge interactions has not been studied. We aim to explore WCFT using the framework of quantum field theory and renormalisation group. We consider scalar fields in the bulk perturbed by a relevant interaction on the edge or the boundary. The goal is to identify the fixed points of WCFTs and understand how they are connected by RG flows from ultaviolet to infrared. The renormalisation of the Lagrangian can be studied using dimensional regularisation. The running of the edge coupling constant, namely the beta function and fixed point can be computed. This will help us compute the correlation functions in presence of running edge couplings using the Feynman diagrams. From the explicit expressions of the bulk one point functions and bulk-edge two point functions we can extract the WCFT data. We will also tune boundary interactions and understand the dependence of the interplay between edge and boundary renormalizations. Our next goal is to understand if these RG flows are irreversible. Can we construct a quantity that is monotonic i.e. the degrees of freedom monotonically decrease under the flow from ultraviolet to infrared? We will approach the problem by computing the entanglement entropy which is a measure of monotonicity. These irreversibility can be proved using techniques the from quantum information theory, based on strong subadditivity of the entanglement entropy. This analysis will provide an information theoretic interpretation of WCFTs. We also aim to investigate the connection between such renormalistion group flows and quantum error correction. It was shown earlier that the fixed points of RG flow are related to quantum error correction codes. We plan to generalise this idea for RG flows in the wedge shaped geometry where the wedge angle plays the role of a parameter in the theory.