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| Paper IPM / P / 15239 |
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| Abstract: | |||||||||
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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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