AI 中文总结
研究二维电子系统中超越平均场的斯托纳转变，应用图解蒙特卡罗算法平等处理阶梯与非阶梯重整化，发现单谷系统低密度下转变条件，双谷系统转变途径受费米子色散各向异性控制。
AI 中文摘要
具有排斥相互作用的费米子的斯托纳不稳定性已在平均场（阶梯）近似下得到充分研究。在本研究中，我们考虑具有一个或两个谷的二维电子系统，并讨论超越阶梯近似的斯托纳转变。在弱耦合下，对阶梯近似的修正主要来自粒子 - 粒子通道中粒子 - 空穴顶点的重整化，且最低阶修正在低密度极限下是对数奇异的。为研究超越最低阶的问题，我们应用图解蒙特卡罗算法并平等对待阶梯和非阶梯重整化。我们发现，在单谷系统中，仅当相互作用携带的动量转移有截止时，在低密度下才会发生向铁磁性的斯托纳转变。在双谷系统中，限制没那么严格。在此我们发现要么直接发生斯托纳转变进入自旋和谷极化状态，要么通过中间谷极化状态发生一组两个斯托纳转变。该路径由费米子色散的各向异性控制。
英文摘要
Stoner instabilities for fermions with repulsive interaction have been well studied within the mean-field (ladder) approximation. In this study, we consider two-dimensional electronic systems with one or two valleys and discuss a Stoner transition beyond the ladder approximation. At weak coupling, the corrections to the ladder approximation come predominantly from the renormalization of the particle-hole vertex in the particle-particle channel, and the lowest-order corrections are logarithmically singular in the low-density limit. To investigate the problem beyond the lowest order, we apply the diagrammatic Monte Carlo algorithm and treat ladder and non-ladder renormalizations on equal footing. We find that in a one-valley system, a Stoner transition to a ferromagnetism occurs at low density only if there is a cutoff on the momentum transfer carried by the interaction. In a two-valley system, the restriction is less severe. Here we find either a direct Stoner transition into a spin- and valley-polarized state, or a set of two Stoner transitions via an intermediate valley-polarized state. The pathway is controlled by the anisotropy of the fermionic dispersion.
Comments35 pages, 17 figures
