@article{AssaadBercxHohenadler2013,
  author    = {Assaad, F. F. and Bercx, M. and Hohenadler, M.},
  title     = {Topological Invariant and Quantum Spin Models from Magnetic pi Fluxes in Correlated Topological Insulators},
  series = {Physical Review X},
  volume    = {3},
  journal   = {Physical Review X},
  number    = {1},
  doi       = {10.1103/PhysRevX.3.011015},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-129849},
  year      = {2013},
  abstract  = {The adiabatic insertion of a \(\pi\) flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that \(\pi\) fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated \(Z_2\) topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a \(\pi\) flux gives rise to a Kramers doublet of spin-fluxon states with a Curie-law signature in the magnetic susceptibility. Electronic correlations also provide a bosonic mode of magnetic excitons with tunable energy that act as exchange particles and mediate a dynamical interaction of adjustable range and strength between spin fluxons. \(\pi\) fluxes can therefore be used to build models of interacting spins. This idea is applied to a three-spin ring and to one-dimensional spin chains. Because of the freedom to create almost arbitrary spin lattices, correlated topological insulators with \(\pi\) fluxes represent a novel kind of quantum simulator, potentially useful for numerical simulations and experiments.},
  language  = {en}
}
@article{AssaadHerbut2013,
  author    = {Assaad, Fakher F. and Herbut, Igor F.},
  title     = {Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice},
  series = {Physical Review X},
  volume    = {3},
  journal   = {Physical Review X},
  number    = {031010},
  doi       = {10.1103/PhysRevX.3.031010},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-129829},
  year      = {2013},
  abstract  = {In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is small, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetrybreaking field and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary-field quantum Monte Carlo algorithm. With our enhanced resolution, we find a direct and continuous quantum phase transition between the semimetallic and the insulating antiferromagnetic states with increase of the interaction. The single-particle gap, measured in units of Hubbard U, tracks the staggered magnetization. An excellent data collapse is obtained by finite-size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.},
  language  = {en}
}