Fluctuationinduced continuous transition and quantum criticality in Dirac semimetals
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 LandauGinzburg paradigm. To this end, we study the quantum phase transition of gapless Dirac fermions coupled to a Z _{3} symmetric order parameter within a GrossNeveuYukawa model in 2+1 dimensions, appropriate for the KekulĂ© transition in honeycomb lattice materials. For this model, the standard LandauGinzburg approach suggests a firstorder transition due to the symmetryallowed 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 firstorder 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:

^{[1]};
^{[2]};
^{[3]}
 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:
 Report Number(s):
 BNL1145362017JA; BNL2079772018JAAM
Journal ID: ISSN 24699950; R&D Project: PO015; KC0202030; TRN: US1800331
 Grant/Contract Number:
 SC0012704; SFB 1238, TP C04
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 11; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 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) (SC22); Natural Sciences and Engineering Research Council of Canada (NSERC); German Research Foundation (DFG)
 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
 OSTI Identifier:
 1412714
 Alternate Identifier(s):
 OSTI ID: 1393285; OSTI ID: 1466622
Classen, Laura, Herbut, Igor F., and Scherer, Michael M.. Fluctuationinduced continuous transition and quantum criticality in Dirac semimetals. United States: N. p.,
Web. doi:10.1103/PhysRevB.96.115132.
Classen, Laura, Herbut, Igor F., & Scherer, Michael M.. Fluctuationinduced 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.. 2017.
"Fluctuationinduced continuous transition and quantum criticality in Dirac semimetals". United States.
doi:10.1103/PhysRevB.96.115132. https://www.osti.gov/servlets/purl/1412714.
@article{osti_1412714,
title = {Fluctuationinduced 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 LandauGinzburg paradigm. To this end, we study the quantum phase transition of gapless Dirac fermions coupled to a Z3 symmetric order parameter within a GrossNeveuYukawa model in 2+1 dimensions, appropriate for the KekulĂ© transition in honeycomb lattice materials. For this model, the standard LandauGinzburg approach suggests a firstorder transition due to the symmetryallowed 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 firstorder 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 = {2017},
month = {9}
}