Scaling at Chiral Clock Criticality via Entanglement Renormalization

TL;DR

This paper uses the MERA tensor network to analyze a critical line in the $ ext{Z}_3$ chiral clock model, revealing how critical exponents evolve with the chiral parameter and demonstrating MERA's effectiveness in capturing complex quantum criticality.

Contribution

The study constructs a MERA representation of the chiral clock model's ground state, extracting critical exponents and scaling data across a range of chiral parameters, highlighting MERA's utility in anisotropic critical systems.

Findings

Effective scaling data varies smoothly with the chiral parameter.

MERA captures the complex low-energy physics of the chiral clock model.

Results are consistent with a slow renormalization group flow between fixed points.

Abstract

We employ the Multiscale Entanglement Renormalization Ansatz (MERA) tensor network to investigate a critical line of continuous quantum phase transitions of the $\mathbb{Z}_3$ chiral clock model. This critical line is believed to be described by a slow renormalization group flow from the 3-state Potts fixed point to another fixed point that features anisotropic scaling of space and time. We use the variational principle to construct a MERA representation of the model's ground state, from which we obtain the ground state energy and the set of scaling operators and their scaling dimensions. These scaling dimensions determine the critical exponents of the model, and we study these critical exponents and other scaling data as a function of the model's chiral parameter. We find a set of effective scaling data that smoothly varies starting from the Potts data as the chiral parameter is increased. Within the context of our approach, we discuss how this result may nevertheless be consistent with the two fixed point hypothesis provided the renormalization group flow is sufficiently slow. Our findings demonstrate MERA's effectiveness in capturing the complex low-energy physics of the chiral clock model and in extracting field theory data for an anisotropic continuum theory.