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TY - THES AU - Weber, Lukas TI - Quantum Monte Carlo methods for critical quantum magnets PB - RWTH Aachen University VL - Dissertation CY - Aachen M1 - RWTH-2022-00746 SP - 1 Online-Ressource : Illustrationen, Diagramme PY - 2022 N1 - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University N1 - Dissertation, RWTH Aachen University, 2022 AB - In this thesis, we study quantum antiferromagnets (AFMs) in three variations.First, we consider dimerized Heisenberg AFMs with open boundary conditions.When the bulk of these systems is quantum critical, also the surface shows criticalfluctuations, which are – in the classical case – well studied within the frameworkof surface critical phenomena. Several quantum magnets, however, show stronglyenhanced surface correlations that are in conflict with the existing theory. Weestablish, using quantum Monte Carlo (QMC) simulations, that this phenomenonappears not only for spin-1/2 but also for spin-1 dimerized AFMs. Furthermore,we check recent predictions for the surface bond correlations in such systems,contributing to a revised understanding of quantum surface critical phenomena.Second, we investigate a model of strongly interacting Dirac fermions, showinga quantum phase transition between an AFM- and a Kekulé-valence-bond-solid-ordered phase. This transition is a candidate for deconfined criticality, i.e. anexotic direct and continuous order-to-order transition beyond the Landau-Ginzburg-Wilson formalism. Using a perturbative mapping to a quantum spin model, weare able to extract the phase diagram with a significantly increased accuracy,resolving two separate transitions and a narrow coexistence phase between thetwo orders that was missed in an earlier study. These results agree with functionalrenormalization group calculations at lower interactions in the fermionic model,where a fermionic multicritical point with emergent enlarged symmetry appears.Finally, we focus on frustrated magnets. Understanding these systems pro-vides a challenge for all unbiased numerical methods. For QMC simulationsthis challenge is the sign problem. However, in magnets with fully frustratedinteractions, sign-problem-free computational basis are exactly known. Here,we study the fully frustrated trilayer (FFTL), which is sign-free in the trimerbasis. The FFTL features a first-order transition emerging at zero temperature andending in a thermal critical point. The shape of this transition depends stronglyon the model parameters, which in an extreme case leads to an extensive jump inground-state entropy across the transition. We find that the shape of the first-orderline has distinct consequences for the specific heat and other observables closeto the thermal critical point. The sign-free bases of fully frustrated models canalso be applied to other frustrated magnets. Here, the sign problem is not avoidedcompletely but can sometimes remain tolerable down to low temperatures. Wereport such results for the square lattice of triangles and the breathing kagomelattice. In the former, we can resolve the ground state ordering tendencies andmake statements about a proposed chirality order in the system. In the kagomelattice, we are restricted to higher temperatures. Nevertheless, we resolve theonset of the frustrated intertrimer-interaction effects. LB - PUB:(DE-HGF)11 DO - DOI:10.18154/RWTH-2022-00746 UR - https://publications.rwth-aachen.de/record/838770 ER -