Using the density-matrix renormalization group method for the ground state and excitations of the Shastry-Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of first-order transitions and a gapless spin liquid phase. The frustrated Shastry-Sutherland model is close to the critical point but slightly inside the spin liquid phase, while previously studied unfrustrated models cross the first-order line. We also argue that recent heat capacity measurements in SrCu$_2$(BO$_3$)$_2$ show evidence of the proposed spin liquid at pressures between 2.6 and 3 GPa.
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