We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to the quantum metric tensor in even dimensions, can be simulated by ultracold atoms in optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find a negative relative magnetoresistance effect with approximately $-B^2$ dependence when a hyperplane cuts through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by introducing an external cyclical parameter in a 3D optical lattice. Moreover, we show that the quantum metric tensor and Berry curvature can be detected by applying an external drive in the optical lattices.

中文翻译：

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张量单极子和光学晶格中的负磁阻效应

我们提出，可以通过光学晶格中的超冷原子模拟一种四维（4D）哈密顿量，该量纲包含与偶数维中的量子度量张量有关的张量单极子。张量单极子的拓扑性质和体界对应关系进行了详细研究。通过将动量沿其中一个维度固定，可以将其简化为有效的三维模型，表现出非平凡的手性绝缘体相。使用半经典的玻尔兹曼方程，我们计算了对磁场的纵向电阻$乙$ 并发现负磁阻效应约为 $-{乙}^2$当一个超平面切穿参数空间中的张量单极子时，它具有依赖性。我们还提出了一种通过在3D光学晶格中引入外部循环参数来实现4D哈密顿量的实验方案。此外，我们表明，可以通过在光学晶格中施加外部驱动来检测量子度量张量和Berry曲率。