Regensburg 2013 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 18: Focused Session: Correlations in Topological Bands (jointly with DS, HL, MA, and O)

TT 18.3: Topical Talk

Montag, 11. März 2013, 16:00–16:30, H20

Hierarchy of Fractional Chern Insulators and Competing Compressible States — •Andreas Läuchli — Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Österreich

The recent engineering of simple tight binding models harboring flat bands with non-zero Chern number calls for a detailed study of the possible many-body phases occurring in partially filled Chern bands and their analogies and differences compared to the continuum Landau level problem. We first report the numerical phase diagram for a flat Chern band with C=1 on the checkerboard lattice, where we find hierarchy multiplets of incompressible states at various fillings ν These are accounted for by an analogy to Haldane pseudopotentials extracted from an analysis of the two-particle problem. Important distinctions to standard fractional quantum Hall physics are striking: absent particle-hole symmetry in a single band, an interaction-induced single-hole dispersion appears, which perturbs and eventually destabilizes incompressible states as ν increases [1]. In second study we investigate the occurrence of fractional Chern insulating phases in a series of bands with higher Chern numbers C=N>1. We find compelling evidence for a series of stable states at ν=1/(2N+1) for fermions as well as bosonic states at ν=1/(N+1). By examining the topological ground state degeneracies and the excitation structure as well as the entanglement spectrum, we conclude that these states are Abelian [2].
[1] A. M. Läuchli, Z. Liu, E.J . Bergholtz, and R. Moessner, arxiv:1207.6094 (2012)
Z. Liu, E. J. Bergholtz, H. Fan, and A. M. Läuchli, Phys. Rev. Lett. 109, 186805 (2012)