Correlations and entanglement in flat band models with variable Chern numbers
arXiv:1407.0329 · doi:10.1088/1742-5468/2014/10/P10012
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 is increasing with , 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 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.
17 pages, 6 figures, submitted to Journal of Statistical Mechanics as a proceedings of ESICQW12
References in corpus (20)
- Non-Abelian Anyons and Topological Quantum Computation
- Topological Field Theory of Time-Reversal Invariant Insulators
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Fractional quantum Hall effect in the absence of Landau levels
- Scalar spin chirality and quantum Hall effect on a triangular lattice
- Flat Chern Band in a Two-Dimensional Organometallic Framework
- A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
- Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
- Topological flat band models with arbitrary Chern numbers
- Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
- Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
- Flat bands with higher Chern number in pyrochlore slabs
- Induced self-stabilization in fractional quantum Hall states of light
- Enhancing the stability of a fractional Chern insulator against competing phases
- Designing Topological Bands in Reciprocal Space
- Momentum-space instantons and maximally localized flat-band topological Hamiltonians
- Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries