We explore the quantum criticality of a two-site model combining quantum Rabi models with hopping interaction. Through a combination of analytical and numerical approaches, we find that the model allows the appearance of a superradiant quantum phase transition (QPT) even in the presence of strong ${\mathbf{A}}^2$ terms, preventing single-site superradiance. In the two-site model the effect of ${\mathbf{A}}^2$ terms can be surmounted by the photon delocalization from hopping, and a reversed superradiant QPT occurs as a consequence of the competition between ${\mathbf{A}}^2$ terms and the hopping interaction. We characterize the phase diagram and scaling functions and extract the critical exponents in the vicinity of the critical point, thus establishing the universal behavior of the second-order phase transition. Remarkably the effective hopping strength will be enhanced if more cavities are cascaded. We also prove that the multiqubit counterpart of the quantum Rabi dimer, i.e., the Dicke dimer, has the same properties in beating the ${\mathbf{A}}^2$ effect. Our work provides a path to the study of phase transitions in the presence of the ${\mathbf{A}}^2$ terms and offers the prospect of investigating quantum-criticality physics and quantum devices in many-body systems.

中文翻译：

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量子Rabi二聚体中超辐射相对A2效应的复原力

我们探索了将量子Rabi模型与跳跃相互作用相结合的两点模型的量子临界性。通过分析和数值方法的组合，我们发现该模型即使出现了强辐射，也允许出现超辐射量子相变（QPT）。${\mathbf{一种}}^2$条款，防止单点超辐射。在两站点模型中的效果${\mathbf{一种}}^2$ 可以通过跳跃使光子离域来克服这些项，并且由于之间的竞争，发生了反向的超辐射QPT。 ${\mathbf{一种}}^2$术语和跳跃交互。我们表征了相图和缩放函数，并提取了临界点附近的临界指数，从而建立了二阶相变的通用行为。明显地，如果级联更多的腔，则有效跳跃强度将得到增强。我们还证明了量子拉比二聚体的多量子位对应物，即狄克二聚体，在击败原子方面具有相同的性质。${\mathbf{一种}}^2$影响。我们的工作为研究存在下的相变提供了一条途径。${\mathbf{一种}}^2$ 术语并为研究多体系统中的量子临界物理学和量子设备提供了前景。