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