Entanglement Renormalization for Weakly Interacting Fields

Understand

We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum.

• A key tool is "quantum circuit perturbation theory," which enables us to systematically construct unitaries that map between wavefunctionals which are Gaussian with arbitrary perturbative corrections.
• As an application, we construct a local, continuous MERA (cMERA) circuit that maps an unentangled scale-invariant state to the ground state of $\varphi^4$ theory to 1-loop.
• Our local cMERA circuit corresponds exactly to 1-loop Wilsonian RG on the spatial momentum modes.