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Paper IPM / Physic / 15240  


Abstract:  
We develop techniques to systematically construct local unitaries which map scaleinvariant,
product state wavefunctionals to the ground states of weakly interacting,
continuum quantum field theories. More broadly, we devise a âquantum circuit perturbation
theoryâ 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 noninteracting examples. Our methods enable the
systematic perturbative calculation of cMERA circuits for weakly interacting theories,
and as a demonstration we compute the 1loop cMERA circuit for scalar phi^4 theory
and analyze its properties. In this case, we show that Wilsonian renormalization of
the spatial momentum modes is equivalent to a local positionspace cMERA circuit.
This example provides new insights into the connection between positionspace and
momentumspace 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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