Dimerized valence bond solids appear naturally in spin-1/2 systems on bipartite lattices, with the geometric frustrations playing a key role both in their stability and the eventual melting due to quantum fluctuations. Here, we ask the question of the stability of such dimerized solids in spin-1 systems, taking the anisotropic square lattice with bilinear and biquadratic spin-spin interactions as a paradigmatic model. The lattice can be viewed as a set of coupled spin-1 chains, which in the limit of vanishing interchain coupling are known to possess a stable dimer phase. We study this model using the density matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS) techniques, supplemented by the analytical mean-field and linear flavor-wave theory calculations. While the latter predicts the dimer phase to remain stable up to a reasonably large interchain-to-intrachain coupling ratio $r\lesssim 0.6$, the DMRG and iPEPS find that the dimer solid melts for much weaker interchain coupling not exceeding $r\lesssim 0.15$. We find the transition into a magnetically ordered state to be first order, manifested by a hysteresis and order parameter jump, precluding the deconfined quantum critical scenario. The apparent lack of stability of dimerized phases in 2D spin-1 systems is indicative of strong quantum fluctuations that melt the dimer solid.

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• First order phase transitions
• Phase diagrams
• Quantum phase transitions
• 2-dimensional systems
• Density matrix renormalization group
• Heisenberg model
• Holstein-Primakoff method
• Projected entangled pair states
• Tensor network methods