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.
Stottmeister, A., Morinelli, V., Morsella, G., Tanimoto, Y. (2021). Operator-algebraic renormalization and wavelets. PHYSICAL REVIEW LETTERS, 127(23) [10.1103/PhysRevLett.127.230601].
Operator-algebraic renormalization and wavelets
Morinelli V.;Morsella G.;Tanimoto Y.
2021-01-01
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.| File | Dimensione | Formato | |
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