Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems

TL;DR

This paper uncovers a hidden electrodynamical structure in pseudo-Hermitian two-level systems, revealing a topological instanton in a 2+1D electromagnetic analogy that quantizes Berry flux jumps, demonstrated in antiferromagnetic magnons.

Contribution

It introduces a novel 2+1D electromagnetic interpretation of Berry curvature in pseudo-Hermitian systems, highlighting a topological instanton and flux quantization.

Findings

Berry curvature maps onto a 2+1D electromagnetic field.

Presence of a topological instanton with quantized flux jump.

Demonstration in a model related to antiferromagnetic magnons.

Abstract

We reveal a hidden electrodynamical structure emerging from a general $2\times2$ 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.