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Paper   IPM / Physic / 15239
School of Physics
  Title:   Entanglement Renormalization for Weakly Interacting Fields
1.  Jordan S. Cotler
2.  M.R. Mohammadi Mozaffar
3.  A. Mollabashi
4.  A. Naseh
  Status:   Published
  Journal: Phys. Rev. D
  Vol.:  99
  Year:  2019
  Pages:   085005
  Supported by:  IPM
We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum eld theories in the continuum. A key tool is 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 phi^4 theory to 1-loop. Our local cMERA circuit corresponds exactly to 1-loop Wilsonian RG on the spatial momentum modes. In other words, we establish that perturbative Wilsonian RG on spatial momentum modes can be equivalently recast as a local cMERA circuit in phi^4 theory, and argue that this correspondence holds more generally. Our analysis also suggests useful numerical ansatzes for cMERA in the non-perturbative regime.

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