  We investigate the impact of the magnetic field generated by colliding nuclei
on heavy quark-antiquark interactions and heavy quark dynamics in the
quark-gluon plasma (QGP). By means of hard-thermal-loop resummation technique
combined with dimension-two gluon condensates, the static heavy quark potential
and heavy quark momentum diffusion coefficient, which incorporate both
perturbative and non-perturbative interactions between heavy quarks and the QGP
medium, are computed beyond the lowest Landau level approximation. We find that
the imaginary part of the heavy quark potential in the magnetic field exhibits
significant anisotropy. Specifically, the absolute value of the imaginary part
is larger when the quark-antiquark separation is aligned perpendicular to the
magnetic field direction, compared to when it is aligned parallel to the
magnetic field direction. The heavy quark momentum diffusion coefficient in the
magnetized QGP medium also becomes anisotropic. As the temperature rises, the
influence of higher Landau levels becomes increasingly significant, resulting
in a decrease in the anisotropy ratio of the heavy quark momentum diffusion
coefficient to values even below 1. At sufficiently high temperatures, this
ratio ultimately approaches 1. The non-perturbative interactions are
indispensable for understanding heavy quark dynamics in the low-temperature
region. We also study the response of viscous quark matter to the magnetic
field and explore its implications for heavy quark potential, thermal decay
widths of quarkonium states, as well as heavy quark momentum diffusion
coefficient.
