论文标题
抗铁磁量子临界金属通过可伸缩杂种蒙特卡洛的非赫兹 - 米利斯缩放
Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
论文作者
论文摘要
据信，许多基于铁的超导体和掺杂电子的铜层的相图的关键组成部分是量子临界点（QCP），在准二维金属中划定了抗铁磁旋转密度波阶的开始。据信，该QCP的通用类别在描述近端的非Fermi液体和超导阶段的描述中起着基本作用。此过渡的最小模型是$ \ mathrm {o}（3）$ spin-ferrimion模型。尽管努力了许多努力，但仍然缺乏对其普遍特性的明确表征。在这里，我们从数字上研究$ \ mathrm {o}（3）$旋转纤维模型，并提取静态和零摩托姆动力学自旋敏感性的缩放指数和功能形式。我们使用新型自动调整程序的混合蒙特卡洛（HMC）算法来做到这一点，这使我们能够研究$ 80 \ times $ 80 $站点的前所未有的大型系统。我们发现与所有以前的结果相反，对赫兹米利斯形式的侵犯很大。 Furthermore, the form that we do observe provides good evidence that the universal scaling is actually governed by the analytically tractable fixed point discovered near perfect ``hot-spot'" nesting, even for a larger nesting window. Our predictions can be directly tested with neutron scattering. Additionally, the HMC method we introduce is generic and can be used to study other fermionic models of quantum criticality, where there is a strong need to simulate large systems.
A key component of the phase diagram of many iron-based superconductors and electron-doped cuprates is believed to be a quantum critical point (QCP), delineating the onset of antiferromagnetic spin-density wave order in a quasi-two-dimensional metal. The universality class of this QCP is believed to play a fundamental role in the description of the proximate non-Fermi liquid and superconducting phases. A minimal model for this transition is the $\mathrm{O}(3)$ spin-fermion model. Despite many efforts, a definitive characterization of its universal properties is still lacking. Here, we numerically study the $\mathrm{O}(3)$ spin-fermion model and extract the scaling exponents and functional form of the static and zero-momentum dynamical spin susceptibility. We do this using a Hybrid Monte Carlo (HMC) algorithm with a novel auto-tuning procedure, which allows us to study unprecedentedly large systems of $80 \times 80$ sites. We find a strong violation of the Hertz-Millis form, contrary to all previous results. Furthermore, the form that we do observe provides good evidence that the universal scaling is actually governed by the analytically tractable fixed point discovered near perfect ``hot-spot'" nesting, even for a larger nesting window. Our predictions can be directly tested with neutron scattering. Additionally, the HMC method we introduce is generic and can be used to study other fermionic models of quantum criticality, where there is a strong need to simulate large systems.
