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Renormalization Group Flows of Hamiltonians Using Tensor Networks

Autor(en)
Matthias Bal, Michael Marien, J. Haegeman, F. Verstraete
Abstrakt

A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015); S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)], we obtain approximate fixed point tensor networks at criticality. Our formalism, however, preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.

Organisation(en)
Quantenoptik, Quantennanophysik und Quanteninformation
Externe Organisation(en)
Ghent University
Journal
Physical Review Letters
Band
118
Anzahl der Seiten
5
ISSN
0031-9007
DOI
https://doi.org/10.1103/PhysRevLett.118.250602
Publikationsdatum
06-2017
Peer-reviewed
Ja
ÖFOS 2012
103015 Kondensierte Materie, 103029 Statistische Physik
Schlagwörter
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/fc303d13-562e-43e9-8406-7b68c74bfca5