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.

NON-FERMI LIQUID BEHAVIOR IN THE SINGLE-IMPURITY MIXED VALENCE PROBLEM

1995 ◽  
Vol 09 (23) ◽  
pp. 1527-1533
Author(s):  
GUANG-MING ZHANG ◽  
ZHAO-BIN SU ◽  
LU YU
Keyword(s):  
Critical Point ◽  
Fermi Liquid ◽  
Mixed Valence ◽  
Quantum Critical Point ◽  
Coulomb Interactions ◽  
Single Impurity ◽  
Liquid Behavior ◽  
New Type ◽  
Quantum Critical ◽  
Fermi Liquid Behavior

An effective Hamiltonian of the Anderson single-impurity model with finite-range Coulomb interactions is derived near a particular limit, which is analogous to the Toulouse limit of the ordinary Kondo problem, and the physical properties around the mixed valence quantum critical point are calculated. At this quantum critical point, the local moment is only partially quenched and X-ray edge singularities are exhibited. Around this point, a new type of non-Fermi liquid behavior is predicted with an extra specific heat C imp ~ T1/4 + AT ln T and spin-susceptibility χ imp ~T−3/4 + B ln T.

scholarly journals Wake and wave resistance on viscous thin films

2016 ◽  
Vol 792 ◽  
pp. 829-849 ◽  
Author(s):  
René Ledesma-Alonso ◽  
Michael Benzaquen ◽  
Thomas Salez ◽  
Elie Raphaël
Keyword(s):  
Pressure Field ◽  
Finite Size ◽  
External Source ◽  
External Pressure ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Pressure Source ◽  
One Dimensional ◽  
Speed Up

The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one- and two-dimensional geometries. In the comoving frame, the imposed pressure field creates a stationary deformation of the interface – a wake – that spatially vanishes in the far region. The shape of the wake and the way it vanishes depend on both the speed and size of the external source and the properties of the film. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in detail. For finite-size pressure disturbances, it increases with the speed, up to a certain transition value, above which a monotonic decrease occurs. The role of the horizontal extent of the pressure field is studied as well, revealing that for a smaller disturbance the latter transition occurs at a higher speed. Eventually, for a Dirac pressure source, the wave resistance either saturates for a one-dimensional geometry, or diverges for a two-dimensional geometry.

scholarly journals Two-Dimensional Fluctuations at the Quantum-Critical Point ofCeCu6−xAux

1998 ◽  
Vol 80 (25) ◽  
pp. 5627-5630 ◽  
Author(s):  
O. Stockert ◽  
H. v. Löhneysen ◽  
A. Rosch ◽  
N. Pyka ◽  
M. Loewenhaupt
Keyword(s):  
Critical Point ◽  
Quantum Critical Point ◽  
Two Dimensional ◽  
Quantum Critical
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