We reveal a hidden electrodynamical structure emerging from a general $2\times 2$ pseudo-Hermitian system that exhibits real spectra. Even when the Hamiltonian does not explicitly depend on time, the Berry curvature can be mapped onto a $2+1$-dimensional electromagnetic field arising from an artificial spacetime instanton, in sharp contrast to the Hermitian systems where the Berry curvature is equivalent to the static magnetic field of a magnetic monopole in three spatial dimensions. The instanton appearing as a spacetime singularity carries a topological charge that quantizes the jump of magnetic flux of the Berry curvature at the time origin. Our findings are demonstrated in a simple example related to antiferromagnetic magnons.

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• Berry curvature
• Electromagnetic field calculations
• Instantons
• Special relativity
• Topological phases of matter
• Non-Hermitian systems
• Geometry