Entanglement and magnetism in high-spin graphene nanodisks

We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional theory with local density approximation or Hartree-Fock methods cannot handle the strong quantum fluctuations. Applying the unbiased density-matrix renormalization group algorithm we calculate the magnetization and entanglement patterns with high accuracy for different interaction strengths and compare them to the mean-field results. With the help of quantum information analysis and subsystem density matrices we reveal that the edges are strongly entangled with each other. We also address the effect of electron and hole doping and demonstrate that the magnetic properties of triangular nanoflakes can be controlled by an electric field, which reveals features of flat-band ferromagnetism. This may open up new avenues in graphene based spintronics.

Figure 1

The energy spectrum of the noninteracting system. The inset shows the investigated system, the circled levels form the degenerate shell at the Fermi level.

Figure 2

Entanglement patterns in a zigzag nanodisk for $U=0$. The magnitude of the mutual information components is encoded using the logarithmic grayscale in the sidebar. The numbers indicate the positions of sites along the one-dimensional DMRG topology.

Figure 3

Similar to Fig. 2 but for $U/t=2$.

Figure 4

The number of mutual information bonds emerging from lattice sites in Fig. 3 taking into account mutual information components larger than ${10}^{-2}$.

Figure 5

The local magnetic moments ($S_i^z$) of the ground for various values of $U$. The magnitudes of up (blue) and down (red) moments are proportional to the area of the circles.

Figure 6

The ground-state spin for $U/t=2$ as a function of filling of the fourfold degenerate shell in Fig. 1. The line is a guide to the eye. The numerical error of $S$ was within the size of the symbols.