Symmetry-respecting real-space renormalization for the quantum Ashkin-Teller model

TL;DR

This paper applies a symmetry-based real-space renormalization group method to analyze the critical behavior of the quantum Ashkin-Teller model, showing broad agreement with conformal field theory predictions and comparable accuracy to complex numerical simulations.

Contribution

It extends a symmetry-respecting real-space RG approach to a more complex quantum spin model with a rich critical structure, demonstrating its effectiveness.

Findings

Critical exponent estimates agree broadly with conformal field theory.

Method accuracy is comparable to advanced numerical simulations near the Ising point.

Accuracy decreases away from the Ising limit.

Abstract

We use a simple real-space renormalization group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the Ising model. Our investigation explores this approach in more generality, in a model where the critical behavior has a richer structure but which reduces to the simpler Ising case at a special point. We demonstrate that the correlation length critical exponent as predicted from this real-space renormalization group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality. Near the Ising special point, the error in the estimated critical exponent from this simple method is comparable to that of numerically-intensive simulations based on much more sophisticated methods, although the accuracy decreases away from the decoupled Ising model point.