Exploring parity magnetic effects through quantum simulation with superconducting qubits

We present a successful realization of four-dimensional semimetal bands featuring tensor monopoles, achieved using superconducting quantum circuits. Our experiment involves the creation of a highly tunable diamond energy diagram with four coupled transmons, and the parametric modulation of their tunable couplers, effectively mapping momentum space to parameter space. This approach enables us to establish a four-dimensional Dirac-like Hamiltonian with fourfold degenerate points. Moreover, we manipulate the energy of tensor monopoles by introducing an additional pump microwave field, generating effective magnetic and pseudoelectric fields and simulating topological parity magnetic effects emerging from the parity anomaly. Utilizing nonadiabatic response methods, we measure the fractional second Chern number for a Dirac valley with a varying mass term, signifying a nontrivial topological phase transition connected to a five-dimensional Yang monopole. Our work lays the foundation for further investigations into higher-dimensional topological states of matter and enriches our comprehension of topological phenomena.