@article{BeyerGothMueller2022,
  author    = {Beyer, Jacob and Goth, Florian and M{\"u}ller, Tobias},
  title     = {Better integrators for functional renormalization group calculations},
  series = {The European Physical Journal B},
  volume    = {95},
  journal   = {The European Physical Journal B},
  number    = {7},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/s10051-022-00378-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-325131},
  year      = {2022},
  abstract  = {We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice t-t' Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.},
  language  = {en}
}
@phdthesis{Goth2015,
  author    = {Goth, Florian},
  title     = {Continuous time quantum Monte Carlo Studies of Quenches and Correlated Systems with Broken Inversion Symmetry},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-118836},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {This thesis deals with quantum Monte Carlo simulations of correlated low dimensional electron systems. The correlation that we have in mind is always given by the Hubbard type electron electron interaction in various settings. To facilitate this task, we develop the necessary methods in the first part. We develop the continuous time interaction expansion quantum algorithm in a manner suitable for the treatment of effective and non-equilibrium problems. In the second part of this thesis we consider various applications of the algorithms. First we examine a correlated one-dimensional chain of electrons that is subject to some form of quench dynamics where we suddenly switch off the Hubbard interaction. We find the light-cone-like Lieb-Robinson bounds and forms of restricted equilibration subject to the conserved quantities. Then we consider a Hubbard chain subject to Rashba spin-orbit coupling in thermal equilibrium. This system could very well be realized on a surface with the help of metallic adatoms. We find that we can analytically connect the given model to a model without spin-orbit coupling. This link enabled us to interpret various results for the standard Hubbard model, such as the single-particle spectra, now in the context of the Hubbard model with Rashba spin-orbit interaction. And finally we have considered a magnetic impurity in a host consisting of a topological insulator. We find that the impurity still exhibits the same features as known from the single impurity Anderson model. Additionally we study the effects of the impurity in the bath and we find that in the parameter regime where the Kondo singlet is formed the edge state of the topological insulator is rerouted around the impurity.},
  subject      = {Elektronenkorrelation},
  language  = {en}
}