Interfacing unbiased quantum Monte Carlo simulations with state-of-the-art analytic continuation techniques, we obtain exact numerical results for dynamical density and spin correlations in the attractive Hubbard model, describing a spin-balanced two-dimensional cold Fermi gas on an optical lattice. We focus on half-filling, where on average one fermion occupies each lattice site, and the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. The coexistence of $\text{U}\left(1\right)$ broken symmetry and the density modulations makes this regime very challenging and interesting for the calculation of dynamical properties. We compare our unbiased results with state-of-the-art generalized random phase approximation calculations: both approaches agree on a well-defined low-energy Nambu-Goldstone collective mode in the density correlations, while the higher energy structures appear to differ significantly. We also observe an interesting high-energy spin mode. We argue that our results provide a robust benchmark for generalized random phase approximation techniques, which are widely considered to be the method of choice for dynamical correlations in Fermi gases. Also, our calculations yield new physical insight into the high-energy behavior of the dynamical structure factor of the attractive Hubbard model, which is a well known prototype lattice model for superconductors and is a fertile field to target the observation of collective modes in strongly correlated systems.

中文翻译：

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光学晶格上铁离子超固体的动力学结构因子

将无偏量子蒙特卡洛模拟与最新的解析连续技术进行接口，我们在有吸引力的哈伯德模型中获得了动态密度和自旋相关性的精确数值结果，描述了光学晶格上自旋平衡的二维冷费米气体。我们专注于半填充，其中平均每个格子位置占据一个费米子，并且系统显示出一个有趣的超固相：一种具有棋盘格密度调制的超流体。共存$\text{ü}（\mathrm{1个}）$对称性的破坏和密度调制使这种机制对于动力学特性的计算非常具有挑战性和趣味性。我们将无偏结果与最新的广义随机相位近似计算进行了比较：两种方法在密度相关性上都明确定义了低能量的Nambu-Goldstone集体模态，而较高的能量结构似乎存在显着差异。我们还观察到了有趣的高能自旋模式。我们认为我们的结果为广义随机相位逼近技术提供了一个可靠的基准，该技术被广泛认为是费米气体中动态相关性的选择方法。此外，我们的计算还为吸引人的Hubbard模型动力学结构因子的高能行为提供了新的物理见解，