Correlations and entanglement in flat band models with variable Chern numbers

Abstract

We discuss a number of illuminating results for tight binding models supporting a band with variable Chern number, and illustrate them explicitly for a simple class of two-banded models. First, for models with a fixed number of bands, we show that the minimal hopping range needed to achieve a given Chern number $C$ is increasing with $C$, and that the band flattening requires an exponential tail of long-range processes. We further verify that the entanglement spectrum corresponding to a real-space partitioning contains $C$ chiral modes and thereby complies with the archetypal correspondence between the bulk entanglement and the edge energetics. Finally, we address the issue of interactions and study the problem of two interacting particles projected to the flattened band as a function of the Chern number. Our results provide valuable insights for the full interacting problem of a partially filled Chern band at variable filling fractions and Chern numbers.

arXiv comment17 pages, 6 figures, submitted to Journal of Statistical Mechanics as a proceedings of ESICQW12

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• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Topological multi-mode waveguide QED
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• Systematic construction of topological flat-band models by molecular-orbital representation
• Interacting bosons in topological optical flux lattices