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arXiv · 1811.05388

Renormalization of lattice field theories with infinite-range wavelets

Pascal Fries·Ignacio Reyes·Johanna Erdmenger·Haye Hinrichsen
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Abstract

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.

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Pascal Fries, Ignacio Reyes, Johanna Erdmenger, Haye Hinrichsen. 2018-11-13. Renormalization of lattice field theories with infinite-range wavelets. https://doi.org/10.1088/1742-5468%2Fab14d8

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