Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an effective Luttinger-liquid theory to show that interactions generate collective excitations with emergent kinetics and fractionalized charge, analogous to properties found in the two-dimensional fractional quantum Hall regime. Observation of these excitations would provide an important platform for exploring exotic quantum states derived solely from interactions.
We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder and the quantum critical point between the Bose-glass and superfluid is determined in the grand canonical ensemble at µ/U = 0 (close to ρ = 0.5), µ/U = 0.375 (close to ρ = 1), and µ/U = 1 as well as in the canonical ensemble at ρ = 0.5 and 1. Particular attention is paid to disorder averaging and it is shown that a large number of disorder realizations is needed in order to obtain reliable results. Typically, more than 100, 000 disorder realizations was used. In the grand canonical ensemble we find Ztc/U = 0.112(1) with µ/U = 0.375, significantly different from previous studies. When compared to the critical point in the absence of disorder (Ztc/U = 0.2385), this result confirms previous findings showing that disorder enlarges the superfluid region. At the critical point we then study the dynamic conductivity.
The smallest fullerene, dodecahedral C 20 , is studied using a one-band Hubbard model parametrized by U / t. Results are obtained using exact diagonalization of matrices with linear dimensions as large as 5.7ϫ 10 9 , supplemented by quantum Monte Carlo. We report the magnetic and spectral properties of C 20 as a function of U / t and investigate electronic pair binding. Solid forms of C 20 are studied using cluster perturbation theory, and evidence is found for a metal-insulator transition at U ϳ 4t. We also investigate the relevance of strong correlations to the Jahn-Teller effect in C 20 .
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