# 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} }

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…

## 3 Citations

### Entanglement conductance as a characterization of a delocalized-localized phase transition in free fermion models

- PhysicsPhysical Review B
- 2019

We study entanglement Hamiltonian (EH) associated with the reduced density matrix of free fermion models in delocalized-localized Anderson phase transition. We show numerically that the structure of…

### Velocity renormalization in graphene: The role of trigonal warping and electron–phonon coupling effects

- Physics
- 2017

We investigate the combined effects of trigonal warping and electron–phonon interactions on the renormalization of the Fermi velocity in graphene. We present an analytical solution to the associated…

### Topological and nontopological features of generalized Su-Schrieffer-Heeger models

- Physics
- 2020

The (one-dimensional) Su-Schrieffer-Heeger Hamiltonian, augmented by spin-orbit coupling and longer-range hopping, is studied at half filling for an even number of sites. The ground-state phase…

## References

SHOWING 1-10 OF 58 REFERENCES

### Entanglement spectra and entanglement thermodynamics of Hofstadter bilayers

- Physics
- 2013

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

- Physics
- 2016

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

- Physics
- 2012

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

- Physics
- 2011

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.

- PhysicsPhysical review letters
- 2010

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

- Physics
- 2012

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

- Physics
- 2011

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.

- PhysicsPhysical review letters
- 2010

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

- Physics
- 2012

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

- Physics
- 2013

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…