AI 中文总结
研究从重整化群拓扑角度审视铜酸盐超导体的动态电荷近藤击穿情形，通过分析耦合RG流方程确定流的相关性质，发现相关不动点不稳定，结合多种方法阐明理论全局结构，指出扩展标度行为不意味稳定临界态，RG拓扑可作临界行为诊断。
AI 中文摘要
在本文中，我们从重整化群（RG）拓扑的角度研究了为铜酸盐超导体提出的动态电荷近藤击穿情形。通过分析控制有效低能理论的耦合RG流方程，我们确定了流的不动点结构、稳定性性质和全局组织。我们发现假定的有限耦合相互作用不动点对于横向于不变临界流形的微扰是不稳定的。因此，一般的RG轨迹表现出失控行为。为了阐明该理论的全局结构，我们将流方程的解析解与数值相图和庞加莱紧致化相结合。该分析表明相互作用不动点表现出边缘相关的不稳定性，产生指数级大但有限的交叉尺度。由此产生的流拓扑与在涨落诱导的弱一级相变中遇到的各向异性驱动的失控流非常相似。在此框架内，表观量子临界区域可以理解为由近临界不动点控制的扩展交叉，而不是由渐近尺度不变性控制。所得结果表明扩展标度行为的存在本身并不意味着存在稳定的相互作用量子临界态。更一般地说，我们的分析表明RG拓扑如何能够为区分强关联量子物质理论中的真正临界性和伪临界行为提供有力的诊断。
英文摘要
In this paper, we examine the dynamical charge-Kondo-breakdown scenario proposed for cuprate superconductors within the perspective of renormalization group (RG) topology. By analyzing the coupled RG flow equations governing the effective low-energy theory, we determine the fixed-point structure, stability properties, and global organization of the flow. We find that the putative finite-coupling interacting fixed point is unstable against perturbations transverse to an invariant critical manifold. As a result, generic RG trajectories exhibit runaway behavior. To elucidate the global structure of the theory, we combine analytical solutions of the flow equations with numerical phase portraits and Poincaré compactification. This analysis reveals that the interacting fixed point exhibits a marginally relevant instability, generating an exponentially large but finite crossover scale. The resulting flow topology closely resembles anisotropy-driven runaway flows encountered in fluctuation-induced weakly first-order transitions. Within this framework, the apparent quantum-critical regime can be understood as an extended crossover controlled by a near-critical fixed point, rather than by asymptotic scale invariance. The results obtained indicate that the existence of extended scaling behavior does not, by itself, imply the presence of a stable interacting quantum critical state. More generally, our analysis demonstrates how RG topology can provide a powerful diagnostic for distinguishing genuine criticality from pseudo-critical behavior in theories of strongly correlated quantum matter.
Comments31 pages, 5 figures
