Monte Carlo study of microscopic models for Néel-to-plaquette VBS transition on 2D square lattice*

The theory of deconfined quantum criticality (DQC) predicts an interesting connection between the Néel and the valence-bond solid (VBS) states, resulting in critical quantum phase transitions beyond the Ginzburg-Landau paradigm with emergent higher symmetry [1].
DQC with columnar VBS (CVBS) phase has been numerically confirmed in microscopic models [2]. Although there are interesting recent proposals on the possibility of the plaquette VBS (PVBS) phase behaving differently from CVBS due to the immobility of the spinons [3], there were no sign-problem free microscopic models that exhibits the Néel-PVBS transition that could be studied in detail.
Here, we construct such a model, and probe the nature of the transition with quantum Monte Carlo simulations. Our results show that the transition is weakly first-order with enhanced SO(5) symmetry, similar to previous results of a system with different symmetry [4].

[1] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. Fisher, Science 303, 1490 (2004).
[2] H. Shao, W. Guo, and A. W. Sandvik, Science 352, 213 (2016).
[3] Y. You, Z. Bi, and M. Pretko, arXiv:1908.08540 (2019).
[4] B. Zhao, P. Weinberg, and A. W. Sandvik, Nature Physics 15, 678 (2019).