We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant 𝑐 electrons hybridizing with a lattice of localized 𝑓 electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of 𝑓 spins by 𝑐 electrons breaks down, so that 𝑓 excitations change their character from somewhat itinerant to mainly localized, while 𝑐 excitations remain itinerant. Building on Phys. Rev. Lett. 101, 256404 (2008), which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, 𝑇FL<𝑇NFL. In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale 𝑇FL decreases toward and vanishes at the KB QCP; at temperatures below 𝑇FL, FL behavior emerges. At 𝑇=0, we find the following properties. The KB transition is continuous. The 𝑓 quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the 𝑓 band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise 𝑐 and 𝑓 electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the 𝑓 self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for 𝑓-electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments.

中文翻译：

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周期性安德森模型的涌现性质：重费米子量子临界性的高分辨率、实频研究


我们使用细胞动力学平均场理论 （CDMFT） 研究周期性安德森模型 （PAM） 中的顺磁量子临界性，并使用数值重整化群 （NRG） 作为集群杂质求解器。PAM 描述了流动 c 电子与局域 f 电子晶格杂化。在零温度下，当杂化通过所谓的近藤击穿量子临界点 （KB QCP） 减少时，它表现出从近藤相到 Ruderman-Kittel-Kasuya-Yosida （RKKY） 相的大量研究量子相变。在那里，c 电子对 f 自旋的近藤筛选分解，因此 f 激发的特性从有点流动变为主要局部，而 c 激发仍然是流动的。建立在物理学之上。Rev. Lett.101， 256404 （2008） 将 KB 跃迁解释为轨道选择性莫特跃迁，我们在这里通过对各种动力学量（磁化率、自能和谱函数）进行高分辨率、实频研究来非常详细地阐明其性质。NRG 使我们能够研究由 QCP 控制并位于两个温标 TFL<TNFL 之间的量子临界机制。在这种状态下，我们在几个动力学敏感性中发现了非费米液体 （NFL） 行为的指纹。令人惊讶的是，CDMFT 的自洽性对于稳定 QCP 和 NFL 制度至关重要。费米液体 （FL） 标度 TFL 向 KB QCP 方向减小并在 KB QCP 处消失;在低于 TFL 的温度下，会出现 FL 行为。 在 T=0 时，我们发现以下属性。KB 转换是连续的。f 准颗粒重量随着从任一侧接近跃迁而不断减小，仅在 KB QCP 处消失。因此，f 波段的准粒重不仅在 Kondo 相中不为零，而且在 RKKY 相中也不为零;因此，FL 准粒子在两相中都包含 c和f 电子。两个相中的费米表面 （FS） 体积不同，这意味着在 KB QCP 处进行 FS 重建。大 FS 近藤相如预期的那样具有两波段结构，而小 FS RKKY 相出乎意料地具有三波段结构。我们详细分析了近藤相和 RKKY 相的准粒子性质，并揭示了它们的差异。FS 重建伴随着 Luttinger 表面的出现，f 自能在该表面上发散。Luttinger 和 Fermi 表面的体积与电荷密度通过广义 Luttinger 和规则相关。我们将小 FS 体积和出现的 Luttinger 表面解释为 RKKY 相中 f 电子分馏的证据。最后，我们计算了霍尔系数和比热的温度依赖性，发现与实验具有良好的定性一致性。