(color online) The schematic of the diamond lattice chain with three legs, a (blue), b (red), and c (green). Note that ε_h and ε_v define the horizontal and vertical tilting while the artificial magnetic field B with the magnetic flux ϕ in a single plaquette (black solid arrows), which is perpendicular to the lattice plane. Lattice sites are designated by the circles with colored solid lines; simply black solid lines indicate sites concerning tunneling of bosons along diverse paths of diamond lattice chain; the yellow shadow rectangle defines the n-th unit cell of the diamond chain, which covers a (blue), b (red), and c (green) sites.