Precision reconstruction of rational CFT from exact fixed point tensor network

TL;DR

This paper provides an explicit analytical construction of fixed-point tensors for 2D rational conformal field theories, enabling precise extraction of conformal data and advancing understanding of critical phenomena.

Contribution

It introduces a novel analytical method to construct fixed-point tensors for 2D rational CFTs using boundary-changing operators, improving accuracy and insight over previous numerical approaches.

Findings

Explicit fixed-point tensors for Ising, Yang-Lee, and Tri-critical Ising models.

BCO descendants form an optimal basis for truncation.

Construction relates to a strange correlator with holographic implications.

Abstract

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 Tri-critical 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 towards understanding CFT in higher dimensions.