Impurity states for resolving topological phases in Kondo Insulators: ArXiv:1402.6774 Resolving intrinsic ground states of different band topologies is difficult, because the order cannot be measured by local measurements. Interestingly, by placing an impurity on the surface of topological Kondo Insulators protected by time-reversal symmetry, we can show the very different echoes from topologically distinct phases due to the single impurity. Quantum Simulation of Novel Spin Phases in Cold Atoms: Science 340 (6132), 583-587 (2013) Nature 484 (7395), 489-492 (2012) Nature communications 2, 377 (2011) Finding ground states in quantum condensed maters is a difficult task when the degrees of freedom scale up. By designing an emulated system with a much better control and tenability, one can emulate the dynamics or ground state properties of quantum condensed matter system at low temperature described by an emergent low-energy Hamiltonian. This is called quantum simulation. Cold ions have been benchmarked to emulate quantum spin models in condensed matter with long-range interaction and frustrated triangular lattices in our work. Theoretical prediction and suggestion on what phases to look for are crucial for experiments in the future. Interaction-Driven Topological Insulators(TIs) on the Kagome and the Decorated Honeycomb Lattices: Phys. Rev. B 82, 075125 (2010) The key to experimental realizations of TIs (at least so far) is strong intrinsic spin-orbit interaction originating from relativistic effects. The topologically nontrivial behavior in these systems is stabilized by a strong spin-orbit coupling which leads to a band inversion. In this work, we focus on interaction driven topological insulators in frustrated lattices at different fillings and explore the conditions where the topological phases can be stabilized. Quantum Vortex Dynamics in Neutral Superfluids: Phys. Rev. A 81, 013609 (2010) A vortex is a topological defects in superfluids. It has been long believed that vortex can be treated as an effective particle with the vortex center as its only degrees of freedom under the assumption that the wave function of the vortex is rigid when the vortex moves. By our studies, we find the gapless excitations of superfluid order screen the vortex and give the vortex an effective mass. On the other hands, the vortex motion can be damped by excitations. For the detailed discussion on the circumstances under which the vortex-particle duality picture can be applied, please check our work. First-Principle Studies of Novel Materials and Heterostructures: Physical Review B 79 (11), 115408 (2008) Physical Review B 88 (12), 125106 (2013) Density functional studies for predicting ground state properties of materials are very powerful tools for quantitative prediction of real materials or the design of materials with certain properties. With the insights from model studies or quantum chemistry, one can search for novel materials with desired properties and check the consistency of the outcome.
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