SO(5) multicriticality in two-dimensional quantum magnets

Since its proposal, the microscopic realization of deconfined quantum criticality (DQC) has been actively debated [1]. DQC theory predicts that the quantum phase transition between the Néel and valence-bond-solid (VBS) phases is generically critical, under certain assumptions. These two phases spontaneously break seemingly unrelated symmetries, making the search for a lattice model that exhibits DQC essential for exploring physics beyond the Ginzburg-Landau paradigm. The JQ model has been a leading candidate, but finite-size scaling anomalies and tensions with conformal bootstrap bounds on critical exponents have hindered a clear understanding.

In this presentation, we will report our recent findings [2], which clarify this long-standing issue. Using large-scale quantum Monte Carlo simulations on the JQ model with an additional term, we expliclty observe the continuous varying of the coexisting Néel and VBS orders at the transition point. Our results suggest the presence of a multicritical point where the first-order jump goes to 0 in the extended phase diagram. We further observe emergent symmetry scalings suggesting that at the multicritical point Néel and VBS orders mix nontrivially, giving rise to an SO(5) multicritical DQC point aligning with recent theoretical predictions [3] and quantitatively matching conformal bootstrap results [4].

We also discuss how these results provide a unified explanation for the weak transitions and emergent symmetries obsewrved in similar models [5] over recent years.

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

[2] JT, S. Hui, B. Zhao, W. Guo, and A. W. Sandvik, arXiv:2405.06607 (2024)

[3] B-B Chen et al., PRL 132, 246503 (2024)

[4] Z. Zhou, L. Hu, W. Zhu, Y-C. He, arXiv 2306.16435 (2023)

[5] JT and A. W. Sandvik, PRR 2, 0334459 (2020)