Fermi 玻璃中的内禀不稳定性
Intrinsic Instabilities in Fermi Glasses
AI总结：
本文研究了无序金属中弱短程相互作用的影响，发现由于Fermi面附近的局域本征态，任意弱的排斥或吸引相互作用都会导致准粒子态不稳定并形成磁矩，表明Fermi玻璃态在任意维度下均具有内禀不稳定性。
摘要：
本文研究了弱、短程相互作用对无序金属的影响。通过分析非相互作用及对应的 Hartree-Fock 单粒子哈密顿量不同本征态间的相互作用矩阵元，我们论证了由于 Fermi 面附近存在局域单粒子本征态，在热力学极限下，对于任意弱（但有限）的排斥相互作用，Fermi 面上的准粒子态都不稳定，倾向于形成磁矩。这一机制与强相互作用 $U\sim W_B$（$W_B=$ 带宽）或量子 Griffiths 效应的情形截然不同，后者中局部磁矩是在与周围耦合较弱的微小局域区域形成的。我们进行了数值模拟以验证分析。我们进一步在 Landau Fermi 液体类型框架下提出，只要准粒子态存在且是局域的，我们的结果就适用于具有弱、短程相互作用的一般电子系统。对于吸引相互作用也获得了类似结果，表明 Fermi 玻璃态在任意维度下均具有内禀不稳定性。
英文摘要：
We study in this paper the effect of weak, short-ranged interaction on disordered metals. Through analysing the interaction matrix elements between different eigenstates of the non-interacting and corresponding Hartree-Fock single-particle Hamiltonian, we argue that as a result of localized single-particle eigenstates around the Fermi surface, the quasi-particle states on the Fermi surface are unstable towards formation of magnetic moments for arbitrary weak (but finite) repulsive interaction in the thermodynamic limit. This is a mechanism very different from the case of strong interaction $U\sim W_B$ ($W_B=$ bandwidth) or the quantum Griffiths effect where local moments are formed at small localized regions where coupling to the surrounding is weak. Numerical simulations are performed to verify our analysis. We further propose within a Landau Fermi-liquid-type framework that our result is applicable for general electronic systems with weak, short-ranged interaction as long as the quasi-particle states exist and are localized. An analogous result is obtained for attractive interaction, suggesting that Fermi glass state is intrinsically unstable in arbitrary dimension.
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