# The first dynamical quantum simulator

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 quantum gases give access to the non-equilibrium dynamics of interacting many-body systems. In the sudden expansion, particles are released into the optical lattice and allowed to expand under the influence of interactions. In this joint collaboration with Immanuel Bloch's group (LMU & MPQ), we report the observation of ballistic dynamics in a strongly interacting system of bosons in a one-dimensional lattice. We explain this effect in terms of non-trivial conservation laws that exist due to the integrability of so-called hard-core bosons. The figure shows density profiles during the expansion, with a very good agreement between experimental (top row) and numerical results (bottom row). Ref.: J.P. Ronzheimer, M. Schreiber, S. Braun, S. Hodgman, S. Langer, I.P. McCulloch, F. Heidrich-Meisner, I. Bloch, U. Schneider, Phys. Rev. Lett. 110, 205301 (2013) more

# Topological order in the kagome model: beyond Landau's paradigm of phase transitions

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))