Abstract: Geometric phase (or Berry phase) has profound implications for the physical behavior of quantum systems. A prototypical scenario is the two-level quantum system, where the Berry phase can be formulated as the magnetic flux emanating from a fictitious magnetic monopole located at the energy-degenerate point in parameter space. If the Hamiltonian becomes explicitly time-dependent, the Berry phase also evolves over time, thereby generating an accompanying electric field by virtue of the Faraday effect. This insight has led to important applications such as the spin-motive force in a moving magnetic texture. Here we explore a hitherto overlooked case: two-level pseudo-Hermitian (PH) quantum systems with real eigenvalues. Our generic model system supports a unique Berry curvature resembling a 2+1 dimensional electromagnetic field, yet it cannot be mapped onto a static magnetic field as in its Hermitian counterpart, even when the PH Hamiltonian does not explicitly depend on time. The key ingredient here is an emergent spacetime metric characterizing the parameter space such that one component of the adiabatic parameter naturally plays the role of time, while the others act as spatial coordinates. Consequently, the electric and magnetic components of the Berry curvature are inherently connected by the 2+1 dimensional Faraday equation in the presence of spacetime singularities—dubbed instantons—which carry quantized topological charges. These topological instantons in (real-spectral) PH quantum systems parallel the role of magnetic monopoles in Hermitian quantum mechanics. Our discovery unifies non-Hermitian Berry phase physics with field-theoretic concepts, offering a novel handle on topology in open and dissipative quantum systems.
Bio: Dr. Ran Cheng obtained his Ph.D. in Physics from the University of Texas at Austin in 2014, followed by a postdoc appointment at Carnegie Mellon University. In 2018, he joined the University of California, Riverside, as an Assistant Professor and was promoted to Associate Professor in 2025. He holds joint appointments in the Departments of Electrical and Computer Engineering, Physics and Astronomy, and Materials Science and Engineering. Dr. Cheng leads a research group in theoretical Condensed Matter Physics with a focus on spintronics, magnetism, and topological materials. He explores a broad range of fundamental physical phenomena and their implications in advanced materials, especially in magnetic topological insulators and antiferromagnetic nanostructures. His research is driven by both experimental insights and mathematical intuitions. His research is supported by the DoD MURI Award, the NSF CAREER Award, funding from the W.M. Keck Foundation, and several intramural grants.