Since its original proposal [1], the existence and microscopic realization of deconfined quantum critical (DQC) points with lattice models has been under extensive debate. Field-theoretic arguments for DQC provide a plausible scenario where the quantum phase transition between a Neel phase and a valence-bond solid phase — two most basic phases of matter in quantum magnetism — will generically be critical (and is dubbed DQC), despite the fact that they are both spontaneous symmetry breaking phases with a priori completely unrelated symmetries. The so-called JQ model has always been a prominent candidate for a microscopic model exhibiting DQC, but anomalous finite-size scalings and violations with conformal bootstrap bounds had hindered conclusive resolution.
In this talk, I will present our recent efforts to clarify this situation. By examining various correlation functions in the JQ model, we show that the DQC point actually has an additional relevant field, which implies the need for extra parameter tuning to arrive at the true DQC point [2]. After observing a clearly first-order transition with emergent SO(5) symmetry in a related JQ-type model [3], we recently conducted a large-scale numerical experiment for the JQ model with an additional parameter that extends the phase diagram [4]. Our results are consistent with the existence of an SO(5) symmetric DQC point in the extended JQ model phase diagram, but only in the sign-problematic region for quantum Monte Carlo. Although the true DQC point is not directly observable, we show how the extrapolated critical exponents match very well with recently calculated values from sophisticated conformal field theoretic fuzzy sphere calculations [5].
[1] T. Senthil et al., Science 303, 1490 (2004)
[2] B. Zhao, JT, and A. Sandvik, PRL 125, 257204 (2020)
[3] JT and A. Sandvik, PRR 2, 033459 (2020)
[4] JT, S. Hui, B. Zhao, W. Guo, and A. Sandvik, arXiv:2405.06607 (2024)
[5] Z. Zhou, L. Hu, W. Zhu, Y-C. He, arXiv:2306.16435 (2023)

Registration: https://forms.gle/dm6YpcafmJCFWkRx5