Gapless spin liquid state and quantum phase diagram in the spin-1/2 J₁-J₂ square Heisenberg model

The spin-1/2 J₁-J₂ square Heisenberg model is one of the most interesting and also challenging quantum spin models, due to the strongly frustrated interactions. It is of the primary candidate models to study quantum spin liquid (QSL). Despite intensively studied in the past 30 years, the nature of the intermediate nonmagnetic phase is still under great debates. Especially, whether the intermediate phase is a QSL is currently a matter of great concern to the community. A recent DMRG calculation suggests that the intermediate region is a valence bond state. However, the DMRG method is essentially a one-dimensional method. Recently, we developed an effiicent and accurate finite projected entangled pair states (PEPS) method, which can deal with a very large system in high precision. With this state-of-the-art tensor network based method, we find it is a spin liquid phase for a large region of the nonmagnetic phase, and spin correlations of the spin liquid decay in a power law form, indicating it is gapless. Methodologically, we give the first solid PEPS calculation beyond DMRG. By comparing with DMRG in details, we provide a direct numerical evidence to explicitly demonstrate the conceptual advantage of PEPS over DMRG for large 2D systems.