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

## 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. Furthermore, 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 realized in graphene.

- Authors:

- Technion-Israel Inst. of Tech., Haifa (Israel). Dept. of Physics
- Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy

- Publication Date:

- Research Org.:
- Rutgers Univ., Piscataway, NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1473977

- Grant/Contract Number:
- FG02-99ER45742

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Nature Communications

- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2041-1723

- Publisher:
- Nature Publishing Group

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Ovdat, O., Mao, Jinhai, Jiang, Yuhang, Andrei, E. Y., and Akkermans, Eric. Observing a scale anomaly and a universal quantum phase transition in graphene. United States: N. p., 2017.
Web. doi:10.1038/s41467-017-00591-8.
```

```
Ovdat, O., Mao, Jinhai, Jiang, Yuhang, Andrei, E. Y., & Akkermans, Eric. Observing a scale anomaly and a universal quantum phase transition in graphene. United States. doi:10.1038/s41467-017-00591-8.
```

```
Ovdat, O., Mao, Jinhai, Jiang, Yuhang, Andrei, E. Y., and Akkermans, Eric. Mon .
"Observing a scale anomaly and a universal quantum phase transition in graphene". United States. doi:10.1038/s41467-017-00591-8. https://www.osti.gov/servlets/purl/1473977.
```

```
@article{osti_1473977,
```

title = {Observing a scale anomaly and a universal quantum phase transition in graphene},

author = {Ovdat, O. and Mao, Jinhai and Jiang, Yuhang and Andrei, E. Y. and Akkermans, Eric},

abstractNote = {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. Furthermore, 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 realized in graphene.},

doi = {10.1038/s41467-017-00591-8},

journal = {Nature Communications},

number = 1,

volume = 8,

place = {United States},

year = {2017},

month = {9}

}

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##
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journal, April 2011

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