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Operator-Algebraic Renormalization and Wavelets
Alexander Stottmeister1, Vincenzo Morinelli2, Gerardo Morsella3
1Institute of Theoretical Physics, University of Hannover, Appelstraße 2, 30167 Hannover, Germany.
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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