1) Identifying experimental relevant models which demonstrate new strong coupling states is one of the central topics in condensed-matter physics. Here, we present "Proof of Principle" evidence of a spin-liquid phase in Mott material with spin 1/2 electron on each kagome lattice. We find that the ground state is a magnetically disordered spin liquid without symmetry breaking. Our research may provide some insight into the exotic behavior found in the newly synthesized herbertsmithite [O.Ofer et al.2006, P.Mendels et al.2007, J.S.Helton et al.2007 ] ZnCu3(OH)6Cl2 systems. Phys. Rev. Lett. 101, 117203 (2008)

2) Dirac fermion system in graphene is studied numerically. In strong magnetic field, a symmetry broken charge density wave is predicted as the ground state in the excited Landau levels. Such a quantum phase is experimentally observable through transport measurements. Phys. Rev. Lett. 100, 116802 (2008)

3) We develop a theoretical framework to to explore the 2D strong coupling phases from controlled numerical and analytical studies in quasi-one-dimension. As a first step we explore itinerant-boson models with a frustrating ring-exchange interaction on the two-leg ladder, searching for signatures of the recently proposed two-dimensional d-wave-correlated Bose liquid (DBL) phase. Phys. Rev. B 78, 054520 (2008)

4) We predict a strong interaction induced odd integer quantum Hall effect in higher Landau levels for graphene electron systems. Phys. Rev. Lett. 99, 196802 (2007)

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