Martin Bercx, Univ. Würzburg.
We studied the Hubbard model on the honeycomb lattice in an external
magnetic field using a saddle-point approximation and numerical quantum
Monte Carlo simulations.
The honeycomb lattice at half filling displays a point like Fermi surface
and the concomitant density of states vanishes. Introducing a magnetic
field changes the Fermi surface geometry towards a circular-like shape and
generates a finite density of states at the Fermi level. Nesting between
up and down spin Fermi surface leads to a Stoner like instability towards
canted antiferromagnetic order. The transition takes the semimetal to an
canted antiferromagnet which is heralded by the opening of a gap in the
excitation spectrum.
The talk is organized as follows. First the model Hamiltonian is studied
on a mean field level which already captures much of the underlying
physics. In the second part the projector quantum Monte Carlo method is
explained and emphasize lies on the stable computation of observables at
T=0. Finally the numerically obtained static and dynamic quantities
including the staggered magnetization and spectral functions are
discussed.