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%0 Thesis
%A Heßelmann, Stephan
%T Quantum critical phenomena in two-dimensional fermion systems
%I RWTH Aachen University
%V Dissertation
%C Aachen
%M RWTH-2020-12182
%P 1 Online-Ressource (xiii, 132 Seiten) : Illustrationen, Diagramme
%D 2020
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2021
%Z Dissertation, RWTH Aachen University, 2020
%X In this thesis I investigate the critical behavior of two-dimensional fermion systems in the vicinity of various phase transitions. While critical phenomena in classical systems have been studied for a long time, quantum phase transitions in fermionic systems have generated a great amount of current interest, contributing to the understanding of, e.g., graphene and high temperature super conductors. This work consists of several projects, most of which focus on the t−V model of spinless fermions on the honeycomb lattice and its phase transitions. The t−V model, at half-filling, features a quantum critical point of the chiral Ising universality class. In contrast to the conventional Ising universality, this transition includes critical fermionic fields that couple to the order parameter field. I study the behavior of thermal Ising transitions in the vicinity of such a quantum phase transition, and explore further universal features. Furthermore, I present a novel approach to characterize critical points by performing a torus spectroscopy analysis. At the critical point, the low-energy gaps of the lattice model form a universal fingerprint of the transition. This fingerprint is not only characteristic of the quantum phase transition in the lattice model, but also connects to fixed points of the Gross-Neveu-Yukawa field theory. To calculate physical observables and energy gaps, I employ quantum Monte Carlo simulations, which only after rather recent developments can be formulated without a sign-problem. Finally, I investigate a parameter regime inaccessible to quantum Monte Carlo by breaking the particle-hole symmetry of the model with a finite chemical potential. This allows for the probing of instabilities towards phases beyond half-filling. To perform the instability analysis, I employ functional renormalization group methods with a Fermi surface patching. This method is unbiased towards potential phases, because it treats instabilities in the particle-hole and particle-particle channels on an equal footing. In addition to the commensurate charge-density-wave instability of the half-filled case, I identify a bond-order instability, located at the van Hove filling, and an f-wave superconducting instability at further doping.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2020-12182
%U https://publications.rwth-aachen.de/record/808616