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Operator-Algebraic Renormalization and Wavelets

Physical Review Letters, ISSN: 1079-7114, Vol: 127, Issue: 23, Page: 230601
2021
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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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