# 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)

In a joint collaboration between the experimental group of Immanuel Bloch and theorists from the Chair for Theoretical Nanophysics, the unusual quasi-condensation of strongly interacting bosons in nonequilibrium was observed and analyzed. This behavior emerges dynamically when an initially trapped gas of bosons is released and allowed to expand into an empty optical lattice. Our work provides an example of a type of quasi long-range order, which typically is a concept used to describe phases of matter in equilibrium with broken symmetries far from equilibrium, thus calling for new guiding principles. The figure (taken from S. Clark's viewpoint in Physics 8, 99 (2015)) .schematically shows the set-up: In the experiment, an ensemble of long one-dimensional lattice chain of potassium atoms (blue spheres) is prepared in a state where lattice sites at the center are filled with precisely one atom each, and the rest is empty. The grey parabolas represent the lattice’s potential wells. Upon lowering the depth of the wells, so the atoms can hop, the atoms ballistically expand to the left and right and bunch up in the momentum states k=±ð∕2a, where a is the lattice spacing. The time-dependent momentum distribution of the atoms illustrates how, from an initially flat profile, two sharp peaks emerge that correspond to the enhanced occupation of these states. For more details, see Vidmar et al., Phys. Rev. Lett. 115, 175301 (2015). 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))