标题： 通过场论重正化群方法，固定点的稳定性在二维Pomeranchuk/Stone不稳定点处从吸引力切换为排斥力。 显示英文标题

标题： Fixed Point Stability Switches from Attractive to Repulsive at 2d Pomeranchuk/Stoner Instabilities via Field-Theoretical RG

摘要： 我们通过场论函数重正化群（RG）研究了一个相互作用的双味费米系统。 每个味，由 $\pm$标记，具有可调实指数 $\alpha>0$的色散关系 $E^{\pm}=c k^{2\alpha}-\mu^\pm$。 有效理论由味内和味间相互作用参数化，保留全局U(1) $\times$ U(1) 对称性，该对称性可以增强到U(2)。 具有U(2)对称性的系统具有费米液体相以及两种可能的不稳定性，分别导致自发的空间旋转或味对称性破缺，分别称为Pomeranchuk和Stoner不稳定性。 本工作的关键发现如下。 Stoner不稳定性具有保留U(2)对称性的RG不动点。 对于 $\alpha<1$，该不动点是吸引的，表明连续转变。 相反，对于 $\alpha>1$，不动点变为排斥的，并且在没有精细调节的情况下，存在逃逸的RG流，导致不连续转变。 具有 $\mu^+\neq \mu^-$ 的 U(1) $\times$ U(1) 对称系统表现出更丰富的物理现象。 此系统存在两种 Pomeranchuk 不稳定性。 在其中一种情况下，当 $\alpha$ 跨越 $1$ 时，非平凡的 RG 不动点的性质从吸引力变为排斥力。 值得注意的是， $\alpha>1$ 处的逃逸流导致过渡时费米面耗尽。 还研究了这些费米液体中的集体模式。 预测了在不稳定处作为连续转变的 $\alpha<1$ 的通用费米面变形比 $\delta\mu^+/\delta\mu^-$，这可以在实验中观察到。 显示英文摘要

摘要： We study an interacting two-flavor fermionic system via field-theoretical functional renormalization group (RG). Each flavor, labeled by $\pm$, has a dispersion of $E^{\pm}=c k^{2\alpha}-\mu^\pm$ with tunable real exponent $\alpha>0$. The effective theory is parametrized by intra-flavor and inter-flavor interactions, preserving global U(1) $\times$ U(1) symmetry, which can be enhanced to U(2). The U(2) symmetric system has a Fermi liquid phase and two possible instabilities, leading to spontaneous spatial rotational or flavor symmetry breaking, known as the Pomeranchuk and Stoner instabilities, respectively. The key discovery of this work is the following. The Stoner instability possesses an RG fixed point that preserves the U(2) symmetry. For $\alpha<1$, this fixed point is attractive, indicating a continuous transition. Conversely, for $\alpha>1$, the fixed point becomes repulsive, and without fine-tuning, there is runaway RG flow, resulting in a discontinuous transition. The U(1) $\times$ U(1) symmetric system, with $\mu^+\neq \mu^-$, exhibits richer physics. This system have two Pomeranchuk instabilities. At one of them, a non-trivial RG fixed point switches its nature from attractive to repulsive as $\alpha$ increases across $1$. Notably, the runaway flow at $\alpha>1$ results in the depletion of a Fermi surface at the transition. Collective modes in these Fermi liquids are also investigated. A universal Fermi surface deformation ratio $\delta\mu^+/\delta\mu^-$ is predicted for $\alpha<1$ at the instability as a continuous transition, which can be observed experimentally.