Abstract: The concept of the deconfined quantum critical point (DQCP) [1] has been controversial and stimulated many numerical simulations of quantum spin models for more than 10 years. The theory of the DQCP predicts a continuous quantum phase transition between the standard Neel antiferromagnet (AFM) and a valenc-bond crystal (VBC) in two dimensions. As the transition is approached from the VBC, a second length scale, which diverges faster than the standard correlation length, governs an emergent U(1) symmetry and the deconfinement length scale of fractional S=1/2 excitations (spinons). I will review the history of the DQCP theory and numerical simulations of the AFM-VBS transition and present recent work [2] suggesting that the DQCP is even more unusual than previously anticipated. The longer length scale affects scaling preoperties more dramatically than in previously known systems with two divergent length scales, and this is the reason for the previously puzzling behaviors found in simulations.

　　[1] T. Senthil et al., Science 303, 1490 (2004).

　　[2] H. Shao, W. Guo, A. W. Sandvik, Science 352, 213 (2016).