# Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals

## Abstract

In this paper, we establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end, we study the quantum phase transition of gapless Dirac fermions coupled to a Z _{3} symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekulé transition in honeycomb lattice materials. For this model, the standard Landau-Ginzburg approach suggests a first-order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have to be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions N _{f}. A nonperturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers and we obtain the critical N _{f}, where the nature of the transition changes. Furthermore, it is shown that for large N _{f} the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. Finally, we compute the criticalmore »

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Division
- Simon Fraser Univ., Burnaby, BC (Canada). Dept. of Physics
- Univ. of Cologne (Germany). Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States); Simon Fraser Univ., Burnaby, BC (Canada); Univ. of Cologne (Germany)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Natural Sciences and Engineering Research Council of Canada (NSERC); German Research Foundation (DFG)

- OSTI Identifier:
- 1412714

- Alternate Identifier(s):
- OSTI ID: 1393285

- Report Number(s):
- BNL-114536-2017-JA

Journal ID: ISSN 2469-9950; R&D Project: PO015; KC0202030; TRN: US1800331

- Grant/Contract Number:
- SC0012704; SFB 1238, TP C04

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 11; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; critical exponents; first order phase transitions; quantum phase transitions; second order phase transitions; Dirac semimetal; graphene; functional renormalization group; particles & fields; statistical physics; condensed matter & materials physics

### Citation Formats

```
Classen, Laura, Herbut, Igor F., and Scherer, Michael M.
```*Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevB.96.115132.

```
Classen, Laura, Herbut, Igor F., & Scherer, Michael M.
```*Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals*. United States. doi:10.1103/PhysRevB.96.115132.

```
Classen, Laura, Herbut, Igor F., and Scherer, Michael M. Wed .
"Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals". United States.
doi:10.1103/PhysRevB.96.115132.
```

```
@article{osti_1412714,
```

title = {Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals},

author = {Classen, Laura and Herbut, Igor F. and Scherer, Michael M.},

abstractNote = {In this paper, we establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end, we study the quantum phase transition of gapless Dirac fermions coupled to a Z3 symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekulé transition in honeycomb lattice materials. For this model, the standard Landau-Ginzburg approach suggests a first-order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have to be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions Nf. A nonperturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers and we obtain the critical Nf, where the nature of the transition changes. Furthermore, it is shown that for large Nf the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. Finally, we compute the critical exponents and predict sizable corrections to scaling for Nf = 2.},

doi = {10.1103/PhysRevB.96.115132},

journal = {Physical Review B},

number = 11,

volume = 96,

place = {United States},

year = {Wed Sep 20 00:00:00 EDT 2017},

month = {Wed Sep 20 00:00:00 EDT 2017}

}

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