The Hall conductivity in correlated electron systems

The Hall conductivity describes the response current perpendicular to the direction of an
applied electric field which occurs in many-electron systems exposed to a transverse
magnetic field. It has been found that in lattice systems this quantity is typically quantized[1]
and corresponds to a topological invariant[2], i.e., the so-called first
Chern number. Such an exact correspondence holds for non-interacting
systems at zero temperature and the effect of correlations on the quantized Hall conductivity
is still unclear. We have calculated the Hall conductivity
in the Hubbard model in a magnetic field by means of dynamical mean field theory (DMFT).
Within this approach all purely local correlation effects are included by means of a local
self-energy. We find that upon increasing the interaction strength between the particles the
size of the quantized plateaus of the Hall conductivity is reduced and eventually vanishes.
This reduction of the Hall conductivity can be explained by a correlation driven shift of
spectral weight to the –otherwise gaped– Fermi level which destroys the exact correspondence
to the topological invariant and, hence, the integer quantum Hall effect.

[1] D. J. Thouless, M. Kohomoto, M. P. Nightingale, and M. den Nijs, PRL 49, 405 (1982).
[2] B. Simon, PRL 51, 2167 (1983).