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.

• Received 4 July 2020
• Revised 29 October 2020
• Accepted 12 November 2020

DOI:https://doi.org/10.1103/PhysRevA.102.053325