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We report on a rigorous operator-algebraic renormalization group scheme and construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory.
1901
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Y. Meyer, Wavelets and operators , Cambridge studies in advanced mathematics, Vol. 37 (Cambridge University Press, 1989)
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S. G. Mallat, Multiresolution approximations and wavelet orthonormal bases of L 2 ( ℝ ) L^{2}(\mathds{R}) , Transactions of the American Mathematical Society 315
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R. Fernández, J. Fröhlich, and A. D. Sokal, Random walks, critical phenomena, and triviality in quantum field theory , Texts and Monographs in Physics (Springer, Berlin, 1992)
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S. R. White and R. M. Noack, Real-space quantum renormalization groups, Physical Review Letters 68
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S. R. White, Density matrix formulation for quantum renormalization groups, Physical review letters 69
1992
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I. Daubechies, Ten Lectures on Wavelets , CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61 (SIAM, 1992)
1992
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S. R. White, Density-matrix algorithms for quantum renormalization groups, Physical Review B 48
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W. M. Koo and H. Saleur, Representations of the Virasoro algebra from lattice models, Nuclear Physics B 426
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2009
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2010
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G. Evenbly and G. Vidal, Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms, New Journal of Physics 12
2010
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2012
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G. K. Brennen, P. Rohde, B. C. Sanders, and S. Singh, Multiscale quantum simulation of quantum field theory using wavelets, Physical Review A: Atomic, Molecular, and Optical Physics 92
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M. E. Fisher, Renormalization group theory: Its basis and formulation in statistical physics, Reviews of Modern Physics 70
1998
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G. Battle, Wavelets and Renormalization , Series in Approximations and Decompositions, Vol. 10 (World World Scientific Publishing Company, 1999)
1999
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2004
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U. Schollwöck, The density-matrix renormalization group, Reviews of Modern Physics 77
2005
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S. Duerr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, and G. Vulvert, Ab-Initio Determination of Light Hadron Masses, Science 322
2008
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2008
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G. Vidal, A Class of Quantum Many-Body States That Can Be Efficiently Simulated, Physical Review Letters 101
2008
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2015
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G. Evenbly and S. R. White, Entanglement Renormalization and Wavelets, Physical Review Letters 116
2016
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J. Kijowski and A. Okołów, A modification of the projective construction of quantum states for field theories, Journal of Mathematical Physics 58
2017
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M. S. Zini and Z. Wang, Conformal Field Theories as Scaling Limit of Anyonic Chains, Communications in Mathematical Physics 363
2018
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G. Evenbly and S. R. White, Representation and design of wavelets using unitary circuits, Physical Review A: Atomic, Molecular, and Optical Physics 97
2018
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A. Milsted and T. J. Osborne, Quantum Yang-Mills theory: An overview of a program, Physical Review D: Particles and Fields 98
2018
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J. Haegeman, B. Swingle, M. Walter, J. Cotler, G. Evenbly, and V. B. Scholz, Rigorous free-fermion entanglement renormalization from wavelet theory, Physical Review X 8
2018
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2019
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2019
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B. Nachtergaele, R. Sims, and A. Young, Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms, Journal of Mathematical Physics 60
2019
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A. Kliesch and R. Koenig, Continuum limits of homogeneous binary trees and the Thompson group, Physical Review Letters 124
2020
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