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Tensor network methods for extracting conformal field theory data from fixed-point tensors and defect coarse graining

Wenhan Guo and Tzu-Chieh Wei

  • C. N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-3840, USA

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Phys. Rev. E 109, 034111 – Published 7 March, 2024

DOI: https://doi.org/10.1103/PhysRevE.109.034111

Abstract

We present a comprehensive study on extracting conformal field theory data using tensor network methods, especially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the classical two-dimensional Ising model near the critical temperature. Utilizing two different methods, we extract operator scaling dimensions and operator product expansion coefficients by introducing defects on the lattice and by employing the fixed-point tensor. We also explore the effects of pointlike defects in the lattice on the coarse-graining process. We find that there is a correspondence between coarse-grained defect tensors and conformal states obtained from the lTRG fixed-point equation. We also analyze the capabilities and limitations of our proposed coarse-graining scheme for tensor networks with pointlike defects, including graph-independent local truncation (GILT) and higher-order tensor renormalization group (HOTRG). Our results provide a better understanding of the capacity and limitations of the tensor renormalization group scheme in coarse-graining defect tensors, and we show that GILT+HOTRG can be used to give accurate two- and four-point functions under specific conditions. We also find that employing the minimal canonical form further improves the stability of the RG flow.

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Outline

Information

Phys. Rev. E 109, 034111– Published 7 March, 2024
  • Received 15 June 2023
  • Revised 25 October 2023
  • Accepted 1 December 2023
Article part of CHORUS
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