1303.7131 (E. Dobardzic et al.)

On the geometrical description of fractional Chern insulators based on
static structure factor calculations    [PDF]

E. Dobardzic, M. V. Milovanovic, N. Regnault

We study the static structure factor of the fractional Chern insulator state. The averaged over Brillouin zone Fubini-Study (quantum distance) metric of the underlying non-interacting quantum system enters the quadratic form with small momenta in the expansion of the single particle part of the static structure factor. The form corresponds to the plasmonic part in the Laughlin case, and thus we find that the averaged over Brillouin zone Fubini-Study metric plays the role of "Landau level" metric in the framework of the geometrical description of fractional quantum Hall systems [F.D.M. Haldane, PRL 107, 116801 (2011)] and an effective (continuum) description of fractional Chern insulators. Assuming Laughlin-like correlations in the two body part of the static structure factor, we discuss the properties of the static structure factor in the long-distance limit, and analyze the conditions that have to be satisfied in order for the FQHE scenario [S.M. Girvin, A.H. MacDonald, and P.M. Platzman, Phys. Rev. B 32, 8458 (1985)] to occur. We discuss the relationship of the (averaged) Fubini-Study metric and Berry curvature, and illustrate their influence and correspondence in Haldane model based fractional Chern insulators.

View original: http://arxiv.org/abs/1303.7131