guest ::
%0 Thesis %A Sushchyev, Alexander %T Quantum Monte Carlo studies of strongly correlated fermion- and spin-systems with competing interactions %I RWTH Aachen University %V Dissertation %C Aachen %M RWTH-2024-05967 %P 1 Online-Ressource : Illustrationen %D 2024 %Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University %Z Dissertation, RWTH Aachen University, 2024 %X In this thesis we study (quantum) phase transitions in fermion and spin systems. In the first part we consider the Hubbard model on the square lattice at half filling. For a more realistic description of real materials with partially screened Coulomb interactions, we include non-local repulsive terms. In detail, we include (i) nearest-neighbor interactions and (ii) long-range Coulomb (LRC) interactions. Based on DQMC simulations within sign-problem free coupling regimes we report results for the temperature resolved double occupancy and entropy, assess a recent study in terms of a first-order metal-to-insulator transition and discuss various phase transitions in the vicinity of the analyzed parameter regime. Continuing DQMC simulations, we examine the Hubbard model on an ABCA stacked tetra-layer graphene structure regarding its magnetic ground state properties over a wide range of the local Hubbard-U. Motivated by experimental findings, we added an extended layer-to-layer interaction and analyzed the extended model in the sign-problem free regime. The second part considers the Heisenberg model regarding different spinexchange interactions, based on SSE simulations. We examine the most generic case of three varying couplings along the unequivalent directions on a honeycomb lattice, where we find anomalous finite-size scaling corrections in the Binder ratio along the quantum phase transition lines between an AFM order and dimerized unordered states. Finally, we extend our Heisenberg model studies to the three-dimensional diamond lattice for both antiferromagnetic as well as ferromagnetic couplings. We determine the finite critical temperatures and find the value of the Néel temperature to be higher than the value for the Curie temperature. We discuss the stability of the ordered phases against thermal fluctuations with respect to the low-temperature entropy gain. %F PUB:(DE-HGF)11 %9 Dissertation / PhD Thesis %R 10.18154/RWTH-2024-05967 %U https://publications.rwth-aachen.de/record/987978