When Feynman proposed quantum computing in 1982, he suggested as one application the simulation of quantum systems that are too hard for analytical methods or classical computers. In this collaboration with the experimental group of Immanuel Bloch (LMU and MPQ) a simulator for the study of the relaxation of a non-equilibrium many-body quantum state towards thermal equilibrium was proposed. While theory allowed the validation of this dynamical quantum simulator without a single free fit parameter, the experiment itself could go way beyond the simulation times reached by the best classical methods, allowing the observation oft he build-up of non-trivial quantum correlations and the thermalization process. Ref.: Trotzky, Chen, Flesch, McCulloch, Schollwöck, Eisert, Bloch, Nature Physics 8, 325 (2012)

Experiments with ultra-cold atomic gases give access to the non-equilibrium dynamics of many-body systems. Here we study a cloud of interacting fermions that expands in an optical lattice after being released from the harmonic trap (the figure shows a typical contour plot of the particle density profile during such an expansion). We show that such a system, described by the Hubbard model, can expand ballistically in one dimension, allowing us to study the expansion velocity as a function of initial conditions. Our predictions for the expansion velocity could be verified in experiments similar to the one by Schneider et al. (Nature Physics 8, 213- (2012)) that was done for the two-dimensional case. Ref.: Langer, Schuetz, McCulloch, Schollwöck, Heidrich-Meisner (Phys. Rev. A 85, 043618 (2012) more

For more than 20 years, the ground state of the kagome model, one of the best-known frustrated quantum magnets, has remained elusive. In the world's largest DMRG simulations to date, we have demonstrated using topological Renyi entanglement entropy that, among the many proposals made over decades, it is overwhelmingly likely that this magnet has as ground state a gapped topological quantum spin liquid of the Z2 variety. Topological ground states in real-world systems have been quite elusive so far, with the exception of the fractional quantum Hall effect. Excitations are anyonic and do not obey conventional Fermi or Bose statistics. At the same time, this magnet does not break locally any symmetry group of the Hamiltonian, as would be the case in conventional Landau theory of phase transitions, but its topological order can only be classified in a global picture of the entire magnet. Ref.: Depenbrock, McCulloch and Schollwöck (Phys. Rev. Lett. 109, 067201 (2012))