Exact renormalization of wave functionals yields continuous MERA

Samuel Goldman, Nima Lashkari, Robert G. Leigh, Mudassir Moosa

Research output: Contribution to journalArticlepeer-review


The exact renormalization group (ERG) is a powerful tool for understanding the formal properties of field theories. By adapting generalized ERG schemes to the flow of wave functionals, we obtain a large class of continuous unitary networks, a special case of which includes a class of Gaussian continuous multiscale renormalization Ansätze (cMERAs). The novel feature of these generalized wave functional ERG schemes is allowing for modifications of the dispersion relation, which drastically changes the entanglement structure of the ultraviolet states. Through our construction, we demonstrate that cMERA can be derived from a more fundamental "microscopic"principle, which amounts to the usual RG principle of path integral independence, suitably adapted to quantum states of the field theory. The establishment of such a principle may provide a path forward for exploring cMERA beyond the free field regime, and for understanding the nature of entanglement renormalization intrinsically in the continuum.

Original languageEnglish (US)
Article number085004
JournalPhysical Review D
Issue number8
StatePublished - Oct 15 2023

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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