# Observing a scale anomaly and a universal quantum phase transition in graphene

## TL;DR

This paper demonstrates the universality of a quantum phase transition involving scale symmetry breaking, providing experimental evidence in graphene for a phenomenon predicted by quantum physics related to anomalies and Efimov physics.

## Contribution

It presents the first experimental evidence of a scale anomaly and a universal quantum phase transition in graphene, linking theoretical predictions to real-world observations.

## Key findings

- Observation of scale anomaly in graphene
- Experimental evidence of quantum phase transition
- Universality of the anomaly across different systems

## Abstract

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe 'Efimov physics'. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive $1/r$ Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realised in graphene.