Fine Grained Tensor Network Methods

Philipp Schmoll, Saeed S. Jahromi, Max Hörmann, Matthias Mühlhauser, Kai Phillip Schmidt, and Román Orús
Phys. Rev. Lett. 124, 200603 – Published 19 May 2020
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Abstract

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2D tensor networks—such as corner transfer matrix renormalization schemes—which are more involved on complex lattice structures. We prove the validity of our approach by numerically computing the ground-state properties of the ferromagnetic spin-1 transverse-field Ising model on the 2D triangular and 3D stacked triangular lattice, as well as of the hardcore and softcore Bose-Hubbard models on the triangular lattice. Our results are benchmarked against those obtained with other techniques, such as perturbative continuous unitary transformations and graph projected entangled pair states, showing excellent agreement and also improved performance in several regimes.

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  • Received 19 November 2019
  • Revised 21 March 2020
  • Accepted 16 April 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.200603

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Philipp Schmoll1, Saeed S. Jahromi2, Max Hörmann3, Matthias Mühlhauser3, Kai Phillip Schmidt3, and Román Orús2,4,5

  • 1Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany
  • 2Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain
  • 3Chair for Theoretical Physics I, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
  • 4Ikerbasque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain
  • 5Multiverse Computing, Pio Baroja 37, 20008 San Sebastián, Spain

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Issue

Vol. 124, Iss. 20 — 22 May 2020

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