  Synchrotron radio emission is being detected from an increasing number of
galaxy clusters. Spectral index images are a powerful tool to investigate the
origin, nature, and connection of these sources with the dynamical state of the
cluster. The aim of this work is to investigate the spectral index distribution
of the radio halo in the galaxy cluster A520, a complex system from an optical,
radio, and X-ray point of view. We present deep Very Large Array observations
in total intensity at 325 and 1400 MHz. We produced and analyzed spectral index
images of the radio halo in this frequency range at a resolution of 39" and 60"
and looked for possible correlations with the thermal properties of the
cluster. We find an integrated radio halo spectral index alpha(325-1400) ~
1.12. No strong radial steepening is present and the spectral index
distribution is intrinsically complex with fluctuations only partially due to
measurement errors. The radio halo integrated spectral index and the cluster
temperature follow the global trend observed in other galaxy clusters although
a strong point-to-point correlation between the spectral index and the thermal
gas temperature has not been observed. The complex morphology in the spectral
index image of the radio halo in A520 is in agreement with the primary models
for radio halo formation. The flatness of the radial profile suggests that the
merger is still ongoing and is uniformly and continuously (re-) accelerating
the population of relativistic electrons responsible of the radio emission even
at large (~ 1 Mpc) distances from the cluster center.
