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@PHDTHESIS{Weber:838770,
author = {Weber, Lukas},
othercontributors = {Weßel, Stefan and Honerkamp, Carsten},
title = {{Q}uantum {M}onte {C}arlo methods for critical quantum
magnets},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2022-00746},
pages = {1 Online-Ressource : Illustrationen, Diagramme},
year = {2022},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2022},
abstract = {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.},
cin = {135620 / 130000},
ddc = {530},
cid = {$I:(DE-82)135620_20140620$ / $I:(DE-82)130000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2022-00746},
url = {https://publications.rwth-aachen.de/record/838770},
}
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