We perform an in-depth investigation of the phase diagram of the $J_1-J_2$ 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 $J_2/J_1=0.535\left(3\right)$, 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 $J_2/J_1=0.535\left(3\right)$ in the model. From the crossing of the first derivative of the energies with $J_2$ for different sizes, we also determine the precise location of the first-order phase transition between the VBS and stripe AFM phases at $J_2/J_1=0.610\left(5\right)$.

Close

PrevNext

View figure in article

• Density matrix renormalization group
• Magnetism
• Quantum many-body systems