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Paper   IPM / P / 15240
School of Physics
  Title:   Renormalization Group Circuits for Weakly Interacting Continuum Field Theories
1.  Jordan S. Cotler
2.  M.R. Mohammadi Mozaffar
3.  A. Mollabashi
4.  A. Naseh
  Status:   Published
  Journal: Fortsch.Phys
  No.:  10
  Vol.:  67
  Year:  2019
  Pages:   1900038
  Supported by:  IPM
We develop techniques to systematically construct local unitaries which map scale-invariant, product state wavefunctionals to the ground states of weakly interacting, continuum quantum field theories. More broadly, we devise a "quantum circuit perturbation theory" to construct local unitaries which map between any pair of wavefunctionals which are each Gaussian with arbitrary perturbative corrections. Further, we generalize cMERA to interacting continuum field theories, which requires reworking the existing formalism which is tailored to non-interacting examples. Our methods enable the systematic perturbative calculation of cMERA circuits for weakly interacting theories, and as a demonstration we compute the 1-loop cMERA circuit for scalar φ4 theory and analyze its properties. In this case, we show that Wilsonian renormalization of the spatial momentum modes is equivalent to a local position space cMERA circuit. This example provides new insights into the connection between position space and momentum space renormalization group methods in quantum field theory. The form of cMERA circuits derived from perturbation theory suggests useful ansatzes for numerical variational calculations.

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