标题： 无约束量子临界点：进展综述 显示英文标题

标题： Deconfined Quantum Critical Point: A Review of Progress

摘要： 无禁闭量子临界点（DQCPs）被提出作为一类连续的量子相变，发生在两种具有不同对称性破缺模式的有序相之间，超越了传统的朗道-金兹堡-威尔逊（LGW）理论框架。在DQCP处，系统表现出涌现的规范场、分数量子激发和增强的对称性。在这里，我们回顾了在凝聚态系统中探索DQCP的最新理论和实验进展。我们首先介绍过去二十年来在DQCP研究中的理论进展，特别是在正方晶格、蜂窝晶格、Kagome晶格和一维自旋链上的磁模型。然后讨论在量子磁系统中实现DQCP的最新进展。实验上，Shastri-Sutherland模型，在SrCu$_2$(BO$_3$)$_2$中实现，为实现DQCP提供了一个特别有前景的平台。该模型固有的磁挫使其在两种不同的对称性破缺状态之间发生相变：一种是键合固体（VBS）相和一种反铁磁Néel相。值得注意的是，SrCu$_2$(BO$_3$)$_2$通过场诱导的玻色-爱因斯坦凝聚提供了首个接近DQCP的实验证据，从VBS态过渡到Néel态。然而，DQCP的直接实验实现仍然是一个重大挑战。尽管如此，它为通过低维量子系统中的量子相变探索涌现现象提供了有希望的平台。 显示英文摘要

摘要： 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.