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Dimerized valence bond solids appear naturally in spin-1/2 systems onbipartite lattices, with the geometric frustrations playing a key role both intheir stability and the eventual `melting' due to quantum fluctuations. Here,we ask the question of the stability of such dimerized solids in spin-1systems, taking the anisotropic square lattice with bilinear and biquadraticspin-spin interactions as a paradigmatic model. The lattice can be viewed as aset of coupled spin-1 chains, which in the limit of vanishing inter-chaincoupling are known to possess a stable dimer phase. We study this model usingthe density matrix renormalization group (DMRG) and infinite projectedentangled-pair states (iPEPS) techniques, supplemented by the analyticalmean-field and linear flavor wave theory calculations. While the latterpredicts the dimer phase to remain stable up to a reasonably largeinterchain-to-intrachain coupling ratio $r \lesssim 0.6$, the DMRG and iPEPSfind that the dimer solid melts for much weaker interchain coupling notexceeding $r\lesssim 0.15$. We find the transition into a magnetically orderedstate to be first order, manifested by a hysteresis and order parameter jump,precluding the deconfined quantum critical scenario. The apparent lack ofstability of dimerized phases in 2D spin-1 systems is indicative of strongquantum fluctuations that melt the dimer solid.

Quantum Melting of Spin-1 Dimer Solid Induced by Inter-chain Couplings