Exact Renormalization and its Application to Quantum States

Abstract: The exact renormalization group (ERG) is a general tool for implementing the Wilsonian idea that physics is independent of our parametrization of the degrees of freedom. In its original formulation, it is simply a manifestation of the invariance of path integrals with respect to the choice of field variable. More recently, ERG methods have been generalized to objects derived from path integrals, such as wavefunctionals. We extend these ideas in two complementary ways which demonstrate the flexibility of ERG

in the context of quantum states. In one scheme which uses multiple regulators, we obtain a class of unitary wavefunctional flows, a subset of which are the so-called continuous MERA networks. In a parallel investigation, we consider the ERG for density operators and find that the non-locality generated along flows introduces non-unitary contributions to the state. The description of this non-unitarity takes the form of a quantum Markov semigroup. These results have a variety of potential applications, such as the construction of interacting and non-unitary cMERA networks, as well as extending our understanding of emergent geometry and renormalization in both holographic and non-holographic contexts.

HEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

( video )

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Purdue HET

Series comments: The recorded talks will be available on YouTube here: www.youtube.com/playlist?list=PLxU3vHZccQj64m9zsQR74D5WP1z1g4t1J

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