We investigate inhomogeneous chiral condensates, such as the so-called dual chiral density wave of dense quark matter, under an external magnetic field at finite real and imaginary chemical potentials. In a model-independent manner, we find that analytic continuation from imaginary to real chemical potential is not possible due to the singularity induced by inhomogeneous chiral condensates at zero chemical potential. From the discussion on the non-analyticity and methods used in lattice QCD simulations, e.g., Taylor expansion, and the analytic continuation with an imaginary chemical potential, it turns out that information on an inhomogeneous chiral condensed phase is missed in the lattice simulations at finite baryon chemical potentials unless the non-analyticity at zero chemical potential is correctly considered. We also discuss an exceptional case without such non-analyticity at zero chemical potential.
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