@phdthesis{Hofmann2020,
  author    = {Hofmann, Johannes Stephan},
  title     = {On the interplay of topology and interaction: A quantum Monte Carlo study},
  doi       = {10.25972/OPUS-20507},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-205071},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {Adding interactions to topological (non-)trivial free fermion systems can in general have four different effects: (i) In symmetry protected topological band insulators, the correlations may lead to the spontaneous breaking of some protecting symmetries by long-range order that gaps the topological boundary modes. (ii) In free fermion (semi-)metal, the interaction could vice versa also generate long-range order that in turn induces a topological mass term and thus generates non-trivial phases dynamically. (iii) Correlation might reduce the topological classification of free fermion systems by allowing adiabatic deformations between states of formerly distinct phases. (iv) Interaction can generate long-range entangled topological order in states such as quantum spin liquids or fractional quantum Hall states that cannot be represented by non-interacting systems. During the course of this thesis, we use numerically exact quantum Monte Carlo algorithms to study various model systems that (potentially) represent one of the four scenarios, respectively. First, we investigate a two-dimensional \$d_{xy}\$-wave, spin-singlet superconductor, which is relevant for high-\$T_c\$ materials such as the cuprates. This model represents nodal topological superconductors and exhibits chiral flat-band edge states that are protected by time-reversal and translational invariance. We introduce the conventional Hubbard interaction along the edge in order to study their stability with respect to correlations and find ferromagnetic order in case of repulsive interaction as well as charge-density-wave order and/or additional \$i\$s-wave pairing for attractive couplings. A mean-field analysis that, for the first time, is formulated in terms of the Majorana edge modes suggests that any order has normal and superconducting contributions. For example, the ferromagnetic order appears in linear superposition with triplet pairing. This finding is well confirmed by the numerically exact quantum Monte Carlo investigation. Second, we consider spinless electrons on a two-dimensional Lieb lattice that are subject to nearest-neighbor Coulomb repulsion. The low energy modes of the free fermion part constitute a spin-\$1\$ Dirac cone that might be gapped by several mass terms. One option breaks time-reversal symmetry and generates a topological Chern insulator, which mainly motivated this study. We employ two flavors of quantum Monte Carlo methods and find instead the formation of charge-density-wave order that breaks particle-hole symmetry. Additionally, due to sublattices of unequal size in Lieb lattices, this induces a finite chemical potential that drives the system away from half-filling. We argue that this mechanism potentially extends the range of solvable models with finite doping by coupling the Lieb lattice to the target system of interest. Third, we construct a system with four layers of a topological insulators and interlayer correlation that respects one independent time-reversal and a unitary \$\mathbb{Z}_2\$ symmetry. Previous studies claim a reduced topological classification from \$\mathbb{Z}\$ to \$\mathbb{Z}_4\$, for example by gapping out degenerate zero modes in topological defects once the correlation term is designed properly. Our interaction is chosen according to this analysis such that there should exist an adiabatic deformation between states whose topological invariant differs by \$\Delta w=\pm4\$ in the free fermion classification. We use a projective quantum Monte Carlo algorithm to determine the ground-state phase diagram and find a symmetry breaking regime, in addition to the non-interacting semi-metal, that separates the free fermion insulators. Frustration reduces the size of the long-range ordered region until it is replaced by a first order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free fermion states into each other. We conclude that the prescribed reduction rules, which often use the bulk-boundary correspondence, are necessary but not sufficient and require a more careful investigation. Fourth, we study conduction electron on a honeycomb lattice that form a Dirac semi-metal Kondo coupled to spin-1/2 degrees of freedom on a Kagome lattice. The local moments are described by a variant of the Balents-Fisher-Girvin model that has been shown to host a ferromagnetic phase and a \$\mathbb{Z}_2\$ spin liquid at strong frustration. Here, we report the first numerical exact quantum Monte Carlo simulation of the Kondo-coupled system that does not exhibit the negative-sign problem. When the local moments form a ferromagnet, the Kondo coupling induces an anti-ferromagnetic mass term in the conduction-electron system. At large frustration, the Dirac cone remains massless and the spin system forms a \$\mathbb{Z}_2\$ spin liquid. Owing to the odd number of spins per unit cell, this constitutes a non-Fermi liquid that violates Luttinger's theorem which relates the Fermi volume to the particle density in a Fermi liquid. This phase is a specific realization of the so called 'fractional Fermi liquid` as it has been first introduced in the context of heavy fermion models.},
  subject      = {Monte-Carlo-Simulation},
  language  = {en}
}
@article{FischerDirksKlaussneretal.2022,
  author    = {Fischer, Jonas and Dirks, Johannes and Klaussner, Julia and Haase, Gabriele and Holl-Wieden, Annette and Hofmann, Christine and Hackenberg, Stephan and Girschick, Hermann and Morbach, Henner},
  title     = {Effect of clonally expanded PD-1\(^h\)\(^i\)\(^g\)\(^h\) CXCR5-CD4+ peripheral T Helper cells on B cell differentiation in the joints of patients with antinuclear antibody-positive juvenile idiopathic arthritis},
  series = {Arthritis \& Rheumatology},
  volume    = {74},
  journal   = {Arthritis \& Rheumatology},
  number    = {1},
  doi       = {10.1002/art.41913},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-256607},
  pages     = {150-162},
  year      = {2022},
  abstract  = {Objective Antinuclear antibody (ANA)-positive juvenile idiopathic arthritis (JIA) is characterized by synovial B cell hyperactivity, but the precise role of CD4+ T cells in promoting local B cell activation is unknown. This study was undertaken to determine the phenotype and function of synovial CD4+ T cells that promote aberrant B cell activation in JIA. Methods Flow cytometry was performed to compare the phenotype and cytokine patterns of PD-1\(^h\)\(^i\)\(^g\)\(^h\)CD4+ T cells in the synovial fluid (SF) of patients with JIA and T follicular helper cells in the tonsils of control individuals. TCRVB next-generation sequencing was used to analyze T cell subsets for signs of clonal expansion. The functional impact of these T cell subsets on B cells was examined in cocultures in vitro. Results Multidimensional flow cytometry revealed the expansion of interleukin-21 (IL-21) and interferon-γ (IFNγ)-coexpressing PD-1\(^h\)\(^i\)\(^g\)\(^h\)CXCR5-HLA-DR+CD4+ T cells that accumulate in the joints of ANA-positive JIA patients. These T cells exhibited signs of clonal expansion with restricted T cell receptor clonotypes. The phenotype resembled peripheral T helper (Tph) cells with an extrafollicular chemokine receptor pattern and high T-bet and B lymphocyte-induced maturation protein 1 expression, but low B cell lymphoma 6 expression. SF Tph cells, by provision of IL-21 and IFNy, skewed B cell differentiation toward a CD21\(^l\)\(^o\)\(^w\)\(^/\)\(^-\)CD11c+ phenotype in vitro. Additionally, SF Tph cell frequencies correlated with the appearance of SF CD21\(^l\)\(^o\)\(^w\)\(^/\)\(^-\)CD11c+CD27-IgM- double-negative (DN) B cells in situ.},
  language  = {en}
}