Details
| Original language | English |
|---|---|
| Article number | 230601 |
| Journal | Physical review letters |
| Volume | 127 |
| Issue number | 23 |
| Publication status | Published - 1 Dec 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.
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In: Physical review letters, Vol. 127, No. 23, 230601, 01.12.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Operator-Algebraic Renormalization and Wavelets
AU - Stottmeister, Alexander
AU - Morinelli, Vincenzo
AU - Morsella, Gerardo
AU - Tanimoto, Yoh
N1 - Funding Information: Helpful discussions with T. Osborne, A. Abdesselam, and M. Fröb are acknowledged by A. S.. We would also like to thank the unknown referees for their careful consideration of our manuscript thereby improving the clarity of the presentation. V. M. and G. M. are partially supported by the European Research Council Advanced Grant No. 669240 QUEST. A. S. was supported by the Humboldt Foundation through a Feodor Lynen Return Fellowship. V. M. was supported by an Assegno di Ricerca dell’Istituto Nazionale di Alta Matematica (INdAM fellowship) and by the Alexander-von-Humboldt Foundation through a Humboldt Research Fellowship for Experienced Researchers hosted by the Mathematics Department, FAU Erlangen-Nürnberg. Y. T. is supported by the Programma per giovani ricercatori, anno 2014 “Rita Levi Montalcini” of the Italian Ministry of Education, University and Research. V. M., G. M. and Y. T. also acknowledge the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome “Tor Vergata”, Grant No. CUP E83C18000100006 and the University of Rome “Tor Vergata” funding scheme “Beyond Borders,” Grant No. CUP E84I19002200005.
PY - 2021/12/1
Y1 - 2021/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85119119216&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2002.01442
DO - 10.48550/arXiv.2002.01442
M3 - Article
VL - 127
JO - Physical review letters
JF - Physical review letters
SN - 0031-9007
IS - 23
M1 - 230601
ER -