scholarly journals The role of electron-electron interactions in two-dimensional Dirac fermions

Science ◽  
2018 ◽  
Vol 361 (6402) ◽  
pp. 570-574 ◽  
Author(s):  
Ho-Kin Tang ◽  
J. N. Leaw ◽  
J. N. B. Rodrigues ◽  
I. F. Herbut ◽  
P. Sengupta ◽  
...  
Keyword(s):  
Dirac Fermions ◽  
Two Dimensional ◽  
Electron Interactions

scholarly journals Comment on “The role of electron-electron interactions in two-dimensional Dirac fermions”

Science ◽  
2019 ◽  
Vol 366 (6470) ◽  
pp. eaav6869 ◽  
Author(s):  
S. Hesselmann ◽  
T. C. Lang ◽  
M. Schuler ◽  
S. Wessel ◽  
A. M. Läuchli
Keyword(s):  
Critical Point ◽  
Quantum Critical Point ◽  
Finite Size ◽  
Numerical Data ◽  
Research Articles ◽  
Fermi Velocity ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Coulomb Interactions

Tang et al. (Research Articles, 10 August 2018, p. 570) report on the properties of Dirac fermions with both on-site and Coulomb interactions. The substantial decrease, up to ~40%, of the Fermi velocity of Dirac fermions with on-site interaction is inconsistent with the numerical data near the Gross-Neveu quantum critical point. This results from an inappropriate finite-size extrapolation.

scholarly journals Response to Comment on “The role of electron-electron interactions in two-dimensional Dirac fermions”

Science ◽  
2019 ◽  
Vol 366 (6470) ◽  
pp. eaav8877
Author(s):  
Ho-Kin Tang ◽  
J. N. Leaw ◽  
J. N. B. Rodrigues ◽  
I. F. Herbut ◽  
P. Sengupta ◽  
...  
Keyword(s):  
Critical Point ◽  
Finite Size ◽  
Numerical Data ◽  
Fermi Velocity ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Zero Energy ◽  
Long Range Interactions ◽  
Rule Out

Hesselmann et al. question one of our conclusions: the suppression of Fermi velocity at the Gross-Neveu critical point for the specific case of vanishing long-range interactions and at zero energy. The possibility they raise could occur in any finite-size extrapolation of numerical data. Although we cannot definitively rule out this possibility, we provide mathematical bounds on its likelihood.

scholarly journals Role of fluctuations in the yielding transition of two-dimensional glasses

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Misaki Ozawa ◽  
Ludovic Berthier ◽  
Giulio Biroli ◽  
Gilles Tarjus
Keyword(s):  
Two Dimensional

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

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