1

1. Perturbation theory   

DPG-Tagung Regensburg 2016,Vortrag TT 44.2: Mi 9. März

Peter Kopietz, Frankfurt(with Anand Sharma, arXiv:1603.01188)

Multi-logarithmic velocity renormalization in graphene

 2. Functional RG      

 

 

3. Multi­logarithmic singularity in velocity 

2

velocity renormalization in graphene

Hofmann, Barnes, Das Sarma 2014 

experiment: Elias,..., Geim 2011 

3

renormalized velocity from field theoretical RG

Gonzalez, Guinea, Vozmediano, 1994review: Kotov, Uchoa, Pereira, Guinea, Castro­Neto, 2012 

●renormalized Fermi velocity at charge neutrality diverges:

●momentum dependent quasiparticle velocity

for identify(Bauer+Rückriegel+ Sharma+PK, 2015)

4

higher orders in perturbation theory:two loop correction

Mishchenko 2007

Vafek+Case 2008

Barnes, Hwang, Throckmorton, Das Sarma, 2014

5

structure of perturbation theory

● at three loop order term appears● powers of do not resum to power law● what is really happening here?

Barnes, Hwang, Throckmorton, Das Sarma, 2014

6

our main result: logarithmic cutoff renormalization

7

bosonized FRG for undoped graphene: momentum transfer cutoff

●low­energy model

●FRG flow equation 

●Dyson­Schwinger equation 

8

FRG flow of vertex correction

9

vertex correction from Ward identity

forward scattering, if Green function is scalar (no matrices):

(Dzyaloshinski, Larkin 1972; Castellani, Di Castro, Metzner 1994) 

for vanishing momenta still valid in graphene:

can also be obtained from FRG flow equation 

10

low-energy truncation

11

static screening approximation

● neglect frequency dependence of polarization

● exact solution in terms of Lambert W-function

12

recovering perturbation theory

● expand in powers of

13

results with dynamic screening

14

summary

● velocity renormalization at Dirac points in graphene due to Coulomb interactions

● effective UV cutoff in log vanishes itself logarithmically

● reconcile RG with perturbative expansion