  The effects of external magnetic fields on monopoles, spectra of the overlap
Dirac operator, instantons, and the mass of the eta-prime meson are examined by
conducting lattice QCD simulations. The uniform external magnetic fields are
applied to gauge field configurations with $N_{f}$ = 2 + 1 flavor quarks. The
bare quark masses are tuned in order to obtain the physical values of the pion
mass and of the ratio $\frac{m_{s}}{m_{u, d}}$. Standard configurations and
configurations with applied external magnetic fields are generated in the color
confinement and deconfinement phases. The intensity of external magnetic fields
varies from $e|B|$ = 0.57 to 1.14 [GeV$^{2}$]. To examine the influence of
external magnetic fields on monopoles, we first calculate the monopole density,
measure the lengths of the monopole loops and compare them with the absolute
value of the Polyakov loops. Next, using the generated configurations, we
compute the eigenvalues and eigenvectors of the overlap Dirac operator, which
preserves exact chiral symmetry. To investigate how external magnetic fields
affect the spectra of the overlap Dirac operator, we compute spectral
densities, compare fluctuations of the eigenvalues of the overlap Dirac
operator with the predictions of random matrix theory, and estimate the number
of instantons and anti-instantons from the topological charges. In addition, we
analyze smearing effects on these observables and chiral symmetry breaking.
Finally, we calculate the decay constant of the pseudoscalar meson, the chiral
condensate, and the square mass of the eta-prime meson using the eigenvalues
and eigenvectors. We then extrapolate the numerical results in the chiral limit
and demonstrate the effects of external magnetic fields on the extrapolation
results. This article presents preliminary results.
