Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel.
Department of Physics, Cornell University, Ithaca, New York 14853, USA.
Phys Rev Lett. 2023 Jun 2;130(22):226001. doi: 10.1103/PhysRevLett.130.226001.
Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly nontrivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the minimal spatial extent of the localized flat-band Wannier wave functions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the nonperturbative nature of the problem, we identify an analytically tractable limit associated with a "small" spatial extent of the Wannier functions and derive a low-energy effective Hamiltonian that can well describe our numerical results. We also provide unambiguous evidence for the violation of any putative lower bound on the zero-temperature superfluid stiffness in geometrically nontrivial flat bands.
预测电子能带猝灭极限下相互作用系统的命运通常是非常复杂的。相互作用和能带几何驱动的量子涨落之间的复杂相互作用可以导致各种基态之间的竞争，例如电荷密度波序和超导性。在这项工作中，我们使用数值精确的量子蒙特卡罗模拟研究了具有连续可调 Fubini-Study 度量的拓扑平凡平带的电子模型，同时存在局域吸引和最近邻排斥。通过改变电子填充和局域平带 Wannier 波函数的最小空间范围，我们获得了许多交织的顺序。这些包括共存电荷密度波序和超导性的相，即超固体。尽管问题具有非微扰性质，但我们确定了与 Wannier 函数的“小”空间范围相关的可分析处理的极限，并推导出了一个低能有效哈密顿量，可以很好地描述我们的数值结果。我们还为几何上非平凡平带中的零温超流硬度的任何假定下限的违反提供了明确的证据。
