Renormalization of lattice field theories with infinite-range wavelets

We present a new exact renormalization approach for quantum lattice models leading to long-range interactions. The renormalization scheme is based on wavelets with an infinite support in such a way that the excitation spectrum at the fixed point coincides with the spectrum of the associated short-ra...

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Bibliographic Details
Published in:Journal of statistical mechanics 2019-06, Vol.2019 (6), p.64001
Main Authors: Fries, Pascal, Reyes, Ignacio, Erdmenger, Johanna, Hinrichsen, Haye
Format: Article
Language:English
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Summary:We present a new exact renormalization approach for quantum lattice models leading to long-range interactions. The renormalization scheme is based on wavelets with an infinite support in such a way that the excitation spectrum at the fixed point coincides with the spectrum of the associated short-range continuum model in an energy range below an upper cutoff imposed by the lattice spacing. As a consequence, the conformal towers of spectrum are exactly realized on the lattice up to a certain energy scale. We exemplify our approach by applying it to free bosons and to free fermions in 1  +  1 dimensions, as well as to the Ising model. The analysis is also motivated by tensor network approaches to the AdS/CFT correspondence since our results may be useful for a qualitatively new construction of holographic duals complementary to previous approaches based on finite-range wavelets.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/ab14d8