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@PHDTHESIS{SnchezdelaPea:754628,
      author       = {Sánchez de la Peña, David},
      othercontributors = {Honerkamp, Carsten and Scherer, Michael M.},
      title        = {{C}ompeting orders in honeycomb {H}ubbard models with
                      nonlocal {C}oulomb interactions : a functional
                      renormalization group approach},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2019-01283},
      pages        = {1 Online-Ressource (121 Seiten) : Illustrationen,
                      Diagramme},
      year         = {2018},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University 2019; Dissertation, RWTH Aachen University, 2018},
      abstract     = {This dissertation focuses on the application of fermionic
                      functional Renormalization Group (fRG) techniques to the
                      study of competing electronic instabilities arising in two
                      dimensional honeycomb lattice systems at low temperatures.
                      We start by developing a new computational scheme within the
                      fRG, named Truncated Unity fRG (TUfRG), which allows to
                      overcome some of the computational limitations of previous
                      schemes like the Exchange Parametrization fRG, specifically
                      in terms of parallel scalability. Making an efficient use of
                      modern multi-core CPU clusters, the TUfRG scheme opens up
                      the possibility for highly resolved calculations of wave
                      vector dependences in the low-energy effective interactions,
                      which are crucial for the correct description of undoped
                      Honeycomb Hubbard models with extended Coulomb interactions.
                      We continue by applying the TUfRG to the undoped Honeycomb
                      Hubbard model with extended Coulomb interactions up to the
                      second nearest neighbour. As expected, the
                      anti-ferromagnetic spin density wave instability appears for
                      a dominant on-siterepulsion between electrons, and charge
                      density waves of different modulations for dominant pure
                      n-th nearest neighbour repulsive interactions. New
                      instabilities towards incommensurate charge density waves
                      take place when non-local density interactions among several
                      bond distances are simultaneously included. The possibility
                      of a topological Mott insulator being the favored tendency
                      for dominating second nearest neighbour interactions is not
                      realized in our results with high momentum resolution. We
                      also include the effect of a second-nearest neighbour
                      hopping in the dispersion relation, and study its impact on
                      the critical scales and critical coupling strength for
                      antiferromagnetic ordering. We finish by considering
                      long-ranged Coulomb interactions on the HoneycombHubbard
                      model. We find that the mutual competition among ordering
                      tendencies triggered by extended interactions acting at
                      different distances is essential for the stability of the
                      semimetallic state. We then submit the system to biaxial
                      strain, and analyze the critical amount of strain necessary
                      to induce a quantum phase transition towards an ordered
                      ground state. We investigate a range of parameters relevant
                      to the realistic graphene material which are not accessible
                      by numerically exact methods. Although a plethora of charge
                      density waves arises under medium-range interactions, we
                      find the antiferromagnetic spin-density wave to be the
                      prevailing instability for long-ranged interactions. The
                      critical strain needed to induce the antiferromagnetic
                      transition turns out to depend mainly on the spatial decay
                      of the bare interactions. We again explore the impact of
                      including a second-nearest neighbour hopping term.},
      cin          = {135510 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)135510_20140620$ / $I:(DE-82)130000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2019-01283},
      url          = {https://publications.rwth-aachen.de/record/754628},
}