Deconfined quantum critical point(DQCP) between Neel state and valence bond solid(VBS) state has been observed in many different theoretical models, including the most famous J-Q model. In this talk, I will discuss the possibility of emergent gapless quantum spin liquid(QSL) near DQCP. By performing the state-of-the-art tensor network state method, specifically, the finite projected entangled pair state (PEPS) algorithm, we study the global phase diagram for both the spin-1/2 J1-J2 and J1-J2-J3 square antiferromagnetic Heisenberg models. We provide very solid evidence that the nature of the intermediate nonmagnetic phase is actually a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. I will also discuss the potential effective field theory for such a gapless QSL state.
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