Renormalization of lattice field theories with infinite-range wavelets

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.

arXiv comment27 pages, 10 figures

References in corpus (14)

• A class of quantum many-body states that can be efficiently simulated
• Entanglement Renormalization and Holography
• An AdS_3 Dual for Minimal Model CFTs
• Liouville theory revisited
• Liouville Field Theory -- A decade after the revolution
• Prospects for perfect actions
• Lattice Wess-Zumino-Witten Model and Quantum Groups
• The Gravity Dual of the Ising Model
• Entanglement renormalization and wavelets
• Lattice QCD with Ginsparg-Wilson fermions
• Domain Wall Fermions and Chiral Gauge Theories
• Exact holographic mapping in free fermion systems
• LATTICE CONFORMAL THEORIES AND THEIR INTEGRABLE PERTURBATIONS
• Generalized Exact Holographic Mapping with Wavelets

Cited by in corpus (2)

• Scaling limits of lattice quantum fields by wavelets
• Wavelet regularization of Euclidean QED