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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
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velocity renormalization in graphene
Hofmann, Barnes, Das Sarma 2014
experiment: Elias,..., Geim 2011
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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)
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higher orders in perturbation theory:two loop correction
Mishchenko 2007
Vafek+Case 2008
Barnes, Hwang, Throckmorton, Das Sarma, 2014
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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
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our main result: logarithmic cutoff renormalization
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bosonized FRG for undoped graphene: momentum transfer cutoff
●lowenergy model
●FRG flow equation
●DysonSchwinger equation
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FRG flow of vertex correction
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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
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low-energy truncation
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static screening approximation
● neglect frequency dependence of polarization
● exact solution in terms of Lambert W-function
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recovering perturbation theory
● expand in powers of
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results with dynamic screening
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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