The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the $s$-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully characterize this expansion, we determine the polarons' effective mass and their coupling parameter, complementing previous studies on their chemical potential. Furthermore, we extract the magnetic susceptibility from low-imbalance data, finding only small deviations from the mean-field prediction. While the mean-field theory predicts a direct transition from a paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results suggest that the partially ferromagnetic phase is stable in a narrow interval of the interaction parameter. This finding calls for further analyses on the effects due to the fixed-node constraint.

中文翻译：

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二维排斥费米气体与人口不平衡的量子蒙特卡罗模拟

通过固定节点扩散蒙特卡罗模拟研究了二维两组分排斥费米气体的基态性质。每个粒子的能量被确定为组件间相互作用强度和种群不平衡的函数。普遍性制度$秒$-波散射长度是通过比较硬盘和软盘电位的结果来确定的。在大不平衡状态下，状态方程被二维极化子的 Landau-Pomeranchuk 泛函很好地描述。为了充分表征这种膨胀，我们确定了极化子的有效质量及其耦合参数，补充了之前对其化学势的研究。此外，我们从低不平衡数据中提取磁化率，发现与平均场预测的偏差很小。虽然平均场理论预测从顺磁相到完全铁磁相的直接转变，但我们的扩散蒙特卡罗结果表明，部分铁磁相在相互作用参数的狭窄区间内是稳定的。