Quantum Monte Carlo studies of spin liquids and correlation induced effects in topological band insulators

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Topology in solid state physics relies on the idea that states of matter can be characterized by global quantities as opposed to local order parameters which encapsulate symmetry breaking. In this grant proposal, we will concentrate on quantum many-body phenomena where topology plays a dominant role. The gapped quantum spin liquid phase recently observed in the Hubbard model on the honeycomb lattice [1] calls for a characterization. Can it be described by a topological order parameter or is it a band insulator in disguise? To tackle this issue we will develop numerical methods to probe for topological degeneracy. We will also modify the model Hamiltonian so as to attempt to adiabatically continue the quantum spin liquid phase to known band-insulating states. One such modification of the Hamiltonian is to include a spin-orbit coupling which drives a transition from the spin liquid phase to a topological band insulator. The resulting Kane-Mele-Hubbard model opens the door to a number of investigations which address the issue of correlation effects in Z2 topological insulators. Here we will focus on two aspects. Correlations in the helical edge states, and the general characterization of Z2 topological insulators in the presence of correlations. The investigations will rely on sign-problem-free auxiliary field quantum Monte Carlo methods, which allow us to exactly compute static and dynamic correlation functions on lattices with up to 18 x 18 unit cells.