Operator-Algebraic Renormalization and Wavelets

Alexander Stottmeister, Vincenzo Morinelli, Gerardo Morsella, and Yoh Tanimoto

Phys. Rev. Lett. 127, 230601 – Published 1 December 2021

Abstract

We report on a rigorous operator-algebraic renormalization group scheme and construct the free field with a continuous action of translations as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets. Causality follows from Lieb-Robinson bounds for harmonic lattice systems. The scheme is related with the multiscale entanglement renormalization ansatz and augments the semicontinuum limit of quantum systems.

Received 13 February 2020
Revised 26 May 2021
Accepted 15 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.230601

Physics Subject Headings (PhySH)

Lattice field theory Mathematical physics Renormalization group

Functional analytical methods Second quantization

Statistical Physics & ThermodynamicsParticles & FieldsGeneral PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Alexander Stottmeister ¹, Vincenzo Morinelli ², Gerardo Morsella ³, and Yoh Tanimoto ³

¹Institute of Theoretical Physics, University of Hannover, Appelstraße 2, 30167 Hannover, Germany
²Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
³Department of Mathematics, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy