Precision Reconstruction of Rational Conformal Field Theory from Exact Fixed-Point Tensor Network

Journal Article · 27 March 2025 · Physical Review. X

DOI: https://doi.org/10.1103/PhysRevX.15.011073 · OSTI ID:2543094

Cheng, Gong ; Chen, Lin ; Gu, Zheng-Cheng ; Hung, Ling-Yan

The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real-space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the “boundary-changing operators” (BCO) on triangles. Our construction fully captures all the real-space RG conditions. We also provide concrete examples, such as Ising, Yang-Lee, and tricritical Ising models, to compute the scaling dimensions explicitly based on the corresponding FP tensor. The BCO descendants turn out to be an optimal basis such that truncation in bond dimensions naturally produces comparable accuracies with the leading existing FP algorithms. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door toward understanding CFT in higher dimensions. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• OSTI ID: 2543094
• Journal Information: Physical Review. X, Journal Name: Physical Review. X Journal Issue: 1 Vol. 15; ISSN PRXHAE; ISSN 2160-3308
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English