  A singular flat band(SFB), a distinct class of the flat band, has been shown
to exhibit various intriguing material properties characterized by a geometric
quantity of the Bloch wave function called the quantum distance. We present a
general construction scheme for a tight-binding model hosting an SFB, where the
quantum distance profile can be controlled. We first introduce how to build a
compact localized state(CLS), a characteristic eigenstate of the flat band,
providing the flat band with a band-touching point, where a specific value of
the maximum quantum distance is assigned. Then, we develop a scheme designing a
tight-binding Hamiltonian hosting an SFB starting from the obtained CLS,
satisfying the desired hopping range and symmetries by applying the
construction scheme. While the scheme can be applied to any dimensions and
lattice structures, we propose several simple SFB models on the square and
kagome lattices. Finally, we establish a bulk-boundary correspondence between
the maximum quantum distance and the boundary modes for the open boundary
condition, which can be used to detect the quantum distance via the electronic
structure of the boundary states.
