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. MoradiJ. 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… 
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References

SHOWING 1-10 OF 58 REFERENCES

Entanglement spectra and entanglement thermodynamics of Hofstadter bilayers

We study Hofstadter bilayers, i.e. coupled hopping models on two-dimensional square lattices in a perpendicular magnetic field. Upon tracing out one of the layers, we find an explicit expression for

Trigonal warping in bilayer graphene: Energy versus entanglement spectrum

We present a mainly analytical study of the entanglement spectrum of Bernal-stacked graphene bilayers in the presence of trigonal warping in the energy spectrum. Upon tracing out one layer, the

Entanglement spectrum and Wannier center flow of the Hofstadter problem

We examine the quantum entanglement spectra and Wannier functions of the square lattice Hofstadter model. Consistent with previous work on entanglement spectra of topological band structures, we find

Bulk-edge correspondence in entanglement spectra

Li and Haldane conjectured and numerically substantiated that the entanglement spectrum of the reduced density matrix of ground-states of time-reversal breaking topological phases (fractional quantum

Nonlocal order in gapless systems: entanglement spectrum in spin chains.

We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high "entanglement energy" levels, from a

Entanglement entropy and spectra of the one-dimensional Kugel-Khomskii model

We study the quantum entanglement of the spin and orbital degrees of freedom in the one- dimensional Kugel-Khomskii model, which includes both gapless and gapped phases, using analytical techniques

The hierarchical structure in the orbital entanglement spectrum of fractional quantum Hall systems

We investigated the non-universal part of the orbital entanglement spectrum (OES) of the ν = 1/3 fractional quantum Hall (FQH) effect ground state using Coulomb interactions. The non-universal part

Entanglement entropy and entanglement spectrum of the Kitaev model.

An exact formula is obtained for the entanglement entropy of the ground state and all excited states of the Kitaev model and a new quantity is proposed to characterize topologically ordered states--the capacity ofEntanglement, which can distinguish the topologically protected gapless entangler spectrum.

Entanglement spectra of the quantum hard-square model: Holographic minimal models

We study the entanglement properties of a quantum lattice-gas model for which we can find the exact ground state (of the Rokhsar-Kivelson type). The ground state can be expressed as a superposition

Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases

We study the entanglement spectrum (ES) and entropy between two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. This problem gives access to the entanglement properties of
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