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Phys Rev Lett. 2007 Aug 17;99(7):070401. Epub 2007 Aug 16.

Flat bands and Wigner crystallization in the honeycomb optical lattice.

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Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.


We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a sqrt[3] x sqrt[3] structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.

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