Absence of spin liquid phase in the J₁-J₂ Heisenberg model on the square lattice

We perform an in-depth investigation of the phase diagram of the J₁-J₂ Heisenberg model on the square lattice. We take advantage of Density Matrix Renormalization Group and Fully-Augmented Matrix Product States methods and reach unprecedented accuracy with large bond dimensions. We utilize excited-level crossing analysis to pinpoint the phase transition points. It was believed before that there exists a narrow spin liquid phase sandwiched by the Néel antiferromagnetic (AFM) and valence bond solid (VBS) phases. Through careful finite size scaling of the level crossing points, we find a direct phase transition between the Néel AFM and VBS phases at J₂/J₁ = 0.535(3), suggesting the absence of an intermediate spin liquid phase. We also provide accurate results for ground state energies for a variety of sizes, from which we find that the transition between the Néel AFM and VBS phases is continuous. These results indicate the existence of a deconfined quantum critical point at J₂/J₁ = 0.535(3) in the model. From the crossing of the first derivative of the energies with J₂ for different sizes, we also determine the precise location of the first order phase transition between the VBS and stripe AFM phases at J₂/J₁=0.610(5).