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Paper IPM / P / 15239  


Abstract:  
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 scaleinvariant state to the ground state of phi^4
theory to 1loop. Our local cMERA circuit corresponds exactly to 1loop 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 nonperturbative regime.
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