Gapless quantum spin liquid and global phase diagram of the spin-1/2 J₁-J₂ square antiferromagnetic Heisenberg model

The nature of the zero-temperature phase diagram of the spin-1/2J₁-J₂ Heisenberg model on a square lattice has been debated in the past three decades, and it remains one of the fundamental problems unsettled in the study of quantum many-body theory. By using the state-of-the-art tensor network method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram of the J₁-J₂ Heisenberg model up to 24×24 sites, we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region 0.56≲J₂/J₁≤0.61 before the system enters the well known collinear antiferromagnetic phase. We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group (DMRG) method through one-to-one direct benchmark for small system sizes, and thus give rise to a very solid PEPS calculation beyond DMRG. Our numerical evidences explicitly demonstrate the huge power of PEPS for highly frustrated spin systems. Finally, an effective field theory is also proposed to understand the physical nature of the discovered gapless QSL and its relation to deconfined quantum critical point (DQCP).