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Theoretical studies of quantum phase transitions have suggested criticalpoints with higher symmetries than those of the underlying Hamiltonian. Here wedemonstrate a surprising emergent symmetry of the coexistence state at astrongly discontinuous phase transition between two ordered ground states. Wepresent a quantum Monte Carlo study of a two-dimensional $S=1/2$ quantum magnethosting the antiferromagnetic (AFM) and plaquette-singlet solid (PSS) statesrecently detected in SrCu$_2$(BO$_3$)$_2$. We observe that the O(3) symmetricAFM order and the Z$_2$ symmetric PSS order form an O(4) vector at thetransition. The control parameter $g$ (a coupling ratio) rotates the vectorbetween the AFM and PSS sectors and there are no energy barriers between thetwo at the transition point $g_c$. This phenomenon may be observable inSrCu$_2$(BO$_3$)$_2$.

Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet