• DOI:10.1088/1742-5468/2016/11/113101
• Corpus ID: 118623297

Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly

@article{Moradi2016EntanglementSO,
  title={Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly},
  author={Zeinab Moradi and Jahanfar Abouie},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2016},
  volume={2016}
}

• Z. Moradi, J. Abouie
• Published 28 May 2016
• Physics
• Journal of Statistical Mechanics: Theory and Experiment

We perform an analytical study of the energy and entanglement spectrum of non-interacting fermionic bilayer honeycomb lattices in the presence of trigonal warping in the energy spectrum, on-site energy difference and uniform magnetic field. Employing single particle correlation functions, we present an explicit form for a layer–layer entanglement Hamiltonian whose spectrum is the entanglement spectrum. We demonstrate that in the absence of trigonal warping, at zero on-site energy difference exact correspondence is established between the entanglement spectrum and energy spectrum of a monolayer which means that the entanglement spectrum perfectly reflects the edge state properties of the bilayer. We also show that trigonal warping breaks down such a perfect correspondence, however, in Γ-K direction in the hexagonal Brillouin zone, their behaviors are remarkably the same for particular relevances of hopping parameters. In the presence of an on-site energy difference the symmetry of the entanglement spectrum is broken with opening an indirect entanglement gap. We also study the effects of a perpendicular magnetic field on both energy and the entanglement spectrum of the bilayer in the presence of trigonal warping and on-site energy difference. We demonstrate that the entanglement spectrum versus magnetic flux has a self similar fractal structure, known as the Hofstadter butterfly. Our results also show that the on-site energy difference causes a transition from the Hofstadter butterfly to a tree-like picture.