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We study Haldanes honeycomb lattice model and a bilayer generalization thereof from the perspective of edge states, entanglement spectra, and Wannier function behavior. For the monolayer model, we obtain the zigzag edge states analytically, and identify the edge state crossing point $k_c$ with where the $f = 1/2$ entanglement occupancy and the half-odd-integer Wannier centers occur. A continuous interpolation between the entanglement states and the Wannier states is introduced. We then construct a bilayer model by Bernal stacking two monolayers coupled by interlayer hopping. We analyze a particular limit of this model where an extended symmetry, related to inversion, is present. The band topology then reveals a break-down of the correspondence between edge and entanglement spectrum, which is analyzed in detail, and compared with the inversion-symmetric Z2 topological insulators which show a similar phenomenon.
e provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t, t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gaples
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 Hall states) contains information about the counti
Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-$frac{1}{2}$ isotropic ($XXX$)
Motivated by the observation of a disordered spin ground state in the $S=3/2$ material Bi$_3$Mn$_4$O$_{12}$NO$_3$, we study the ground state properties and excitation spectra of the $S=3/2$ (and for comparison $S=1/2$) bilayer Heisenberg model on the
Within this paper we outline a method able to generate truly minimal basis sets which describe either a group of bands, a band, or even just the occupied part of a band accurately. These basis sets are the so-called NMTOs, Muffin Tin Orbitals of orde