  We study the spin-$1/2$ two-dimensional Shastry-Sutherland spin model by
exact diagonalization of clusters with periodic boundary conditions. We develop
an improved level spectroscopic technique using energy gaps between states with
different quantum numbers. The crossing points of some of the relative
(composite) gaps have much weaker finite-size drifts than the normally used
gaps defined only with respect to the ground state, thus allowing precise
determination of quantum critical points even with small clusters. Our results
support the picture of a spin liquid phase intervening between the well known
plaquette-singlet and antiferromagnetic ground states, with phase boundaries in
almost perfect agreement with a recent density matrix renormalization group
study, where much larger cylindrical lattices were used [J. Yang et al., Phys.
Rev. B {\bf 105}, L060409 (2022)]. The method of using composite low-energy
gaps to reduce scaling corrections has potentially broad applications in
numerical studies of quantum critical phenomena.
