There is a number of contradictory findings with regard to whether the theory describing easy-plane quantum antiferromagnets undergoes a second-order phase transition. The traditional Landau-Ginzburg-Wilson approach suggests a first-order phase transition, as there are two different competing order parameters. On the other hand, it is known that the theory has the property of self-duality which has been connected to the existence of a deconfined quantum critical point (DQCP). The latter regime suggests that order parameters are not the elementary building blocks of the theory, but rather consist of fractionalized particles that are confined in both phases of the transition and only appear—deconfine—at the critical point. Nevertheless, many numerical Monte Carlo simulations disagree with the claim of a DQCP in the system, indicating instead a first-order phase transition. Here we establish from exact lattice duality transformations and renormalization group analysis that the easy-plane ${\mathrm{CP}}^1$ antiferromagnet does feature a DQCP. We uncover the criticality starting from a regime analogous to the zero temperature limit of a certain classical statistical mechanics system which we therefore dub frozen. At criticality our bosonic theory is dual to a fermionic one with two massless Dirac fermions, which thus undergoes a second-order phase transition as well.

中文翻译：

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冷冻解禁量子临界

关于描述易平面量子反铁磁体的理论是否经历二阶相变，存在许多相互矛盾的发现。传统的 Landau-Ginzburg-Wilson 方法建议进行一阶相变，因为存在两个不同的竞争顺序参数。另一方面，众所周知，该理论具有自对偶性，这与去约束量子临界点 (DQCP) 的存在有关。后一种情况表明，有序参数不是该理论的基本组成部分，而是由分馏粒子组成，这些粒子在转变的两个阶段都受到限制，并且只在临界点出现——解除限制。然而，许多数值蒙特卡罗模拟不同意系统中 DQCP 的声明，相反，指示一阶相变。在这里，我们从精确的格子对偶变换和重整化群分析中确定易平面${\mathrm{CP}}^{\mathrm{1个}}$反铁磁体确实具有 DQCP。我们从类似于某个经典统计力学系统的零温度极限的状态开始揭示临界性，因此我们将其称为冻结状态。在临界点，我们的玻色子理论与具有两个无质量狄拉克费米子的费米子理论对偶，因此也经历了二阶相变。