Year: 2026
Type: preprint
Abstract: Renormalization group (RG) is a core concept from statistical mechanics to quantum field theory, yet its schemes differ widely across literature. We formulate Wilsonian RG for generic, including finite-dimensional, quantum systems as a quantum channel combining coarse graining with isometric rescaling, whose Kraus representation yields pure conditional trajectories for pure inputs and recovers mixed-state flows upon averaging. We then develop an algebraic extension without assuming tensor-product factorization: the retained low-energy algebra is constructed from the one-particle spectrum, and coarse graining is a conditional expectation onto it. Identifying the channel's Cesàro mean with a resource-destroying map onto fixed states establishes a resource theory of RG and yields a relative-entropy monotone without variational optimization. For thermal states in the zero-temperature limit, the resulting Bogoliubov--Kubo--Mori metric per unit spacetime volume is proportional to the Zamolodchikov metric, directly relating the resource density to $c-c_{\rm IR}$ near a two-dimensional IR fixed point. We also introduce the relative entropy of coarse graining to measure discarded UV information, prove its monotonicity along successive coarse grainings, and evaluate it holographically in global $\mathrm{AdS}_3$.
Source: arXiv (Cornell University)
Authors: Mori, Takato, Nagasawa, Teruaki
Institutions: Rikkyo University, RIKEN, Kanazawa University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214618729