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TY - THES AU - Sánchez de la Peña, David TI - Competing orders in honeycomb Hubbard models with nonlocal Coulomb interactions : a functional renormalization group approach PB - RWTH Aachen University VL - Dissertation CY - Aachen M1 - RWTH-2019-01283 SP - 1 Online-Ressource (121 Seiten) : Illustrationen, Diagramme PY - 2018 N1 - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2019 N1 - Dissertation, RWTH Aachen University, 2018 AB - 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. LB - PUB:(DE-HGF)11 DO - DOI:10.18154/RWTH-2019-01283 UR - https://publications.rwth-aachen.de/record/754628 ER -