  Noncollinear and noncoplanar magnetic orders lead to unusual electronic
structures and transport properties. We here investigate two types of
multiple-Q magnetically ordered states and a topological phase transition
between them in two dimensions. One is a coplanar but noncollinear double-Q
state on a square lattice, which is a semimetal accommodating massless Dirac
electrons. The other is a noncoplanar triple-Q state on a triangular lattice,
which is a Chern insulator showing the quantum anomalous Hall effect. We
discuss the peculiar electronic structures in these two multiple-Q states in a
unified way on the basis of the Kondo lattice model, which suggests a quantum
phase transition between the two states in a continuous change of lattice
geometry between the square and triangular lattices. We systematically examine
the possibility of such a transition by using the mean-field approximation for
the ground state of the periodic Anderson model. After clarifying the parameter
region in which the double-Q (triple-Q) state is stabilized on the square
(triangular) lattice, we show that a continuous topological phase transition
indeed takes place between the double-Q Dirac semimetal and the triple-Q Chern
insulator on the square-to-triangular lattice. The nature of the transition is
discussed by the topologically-protected edge states as well as the bulk
magnetic and electronic properties. The results indicate that unusual critical
phenomena may occur at finite temperature related with multiple-Q chiral
spin-liquid states.
