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  • Letter
  • Open Access

Bond-weighted tensor renormalization group

Daiki Adachi1, Tsuyoshi Okubo2,3, and Synge Todo1,2,4

  • 1Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
  • 2Institute for Physics of Intelligence, University of Tokyo, Tokyo 113-0033, Japan
  • 3JST, PRESTO, Kawaguchi 332-0012, Japan
  • 4Institute for Solid State Physics, University of Tokyo, Kashiwa, 277-8581, Japan

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Phys. Rev. B 105, L060402 – Published 3 February, 2022

DOI: https://doi.org/10.1103/PhysRevB.105.L060402

Abstract

We propose an improved tensor renormalization-group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the conventional TRG and the higher-order tensor renormalization group with the same bond dimension, whereas its computation time is almost the same as that of TRG. Furthermore, BTRG can have nontrivial fixed-point tensors at an optimal hyperparameter. We demonstrate that the singular value spectrum obtained by BTRG is invariant under the renormalization procedure in the case of the two-dimensional Ising model at the critical point. This property indicates that BTRG performs the tensor contraction with high accuracy whereas keeping the scale-invariant structure of tensors.

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Outline

Information

Phys. Rev. B 105, L060402– Published 3 February, 2022
  • Received 18 November 2020
  • Revised 27 December 2021
  • Accepted 5 January 2022
Article part of CHORUS
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