Deconfined Quantum Critical Point: A Review of Progress

Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu$_2$(BO$_3$)$_2$, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a N\'{e}el antiferromagnetic phase. Remarkably, SrCu$_2$(BO$_3$)$_2$ has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the N\'{e}el state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.