  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 electric field, which reveals features of
flat-band ferromagnetism. This may open up new avenues in graphene based
spintronics.
