On the exact renormalization of states in quantum field theories

The study of renormalization is a cornerstone of our modern understanding of quantum field theory and many body physics. As quantum information becomes an increasingly important tool in our understanding of continuum theories, new techniques are needed to understand how renormalization interacts with the strictly quantum features of field theories. By using path integral methods, we can port our understanding of the renormalization of Euclidean field theories to states of the QFT Hilbert space. Such constructions require the use of manifolds with boundary in the path integral, presenting technical and conceptual problems in the usual implementation of the renormalization group (RG). The solution to these problems are not necessarily unique, and in this work we explore two distinct approaches with largely different qualitative behavior. First, we consider half space path integrals with specially modified regulating schemes. The resulting renormalization group flows result in a class of unitary flows which are designed to capture the behavior of a class of continuous entanglement renormalization schemes known as the continuous multiscale renormalization ansatz (cMERA). Then, we consider a renormalization scheme which is in some sense “minimally” modified from a standard renormalization approach of Polchinski, and demonstrate that the resulting ERG flows are described by a non-unitary quantum channels generated by a Lindbladian which we derive. We solve the resulting Lindblad equation for Gaussian density matrices and compute the flow equation to second order in perturbation theory for a φ4 self interaction. We also calculate channel monotones such as the relative entropy and fidelity of ground states flowing under the RG.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Goldman, Samuel

Contributors dc:contributor

• Leigh, Robert
• Faulkner, Thomas
• Hughes, Taylor
• Kahn, Yonatan

• Renormalization
• Open quantum systems

Statement dc:rights

• Copyright 2025 Samuel Goldman

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132469

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132469