Quantum geometry lens shines new light on solids
- 9 hours ago
- 2 min read
A new approach to looking at solids provides theoretical limits on some of their properties
Two RIKEN physicists have established new theoretical limits for experimentally measurable quantities by viewing solids through a lens of quantum geometry1. Their results shed light both on the physics of solids and on quantum mechanics.
The usual approach to studying a solid in physics is to consider all the interactions acting between its atoms or molecules and then use the laws of quantum mechanics to determine the solid’s properties.
But a new methodology involves considering the ‘quantum geometry’ of a solid. It entails studying the geometric structures that arise not in physical space, but in the space of quantum states.
One of the key concepts in this approach is the quantum geometric tensor—a matrix that contains information about the distances and curvatures of quantum states.
Physicists are always eager to establish bounds for quantities as they provide fundamental insights into systems and the physics governing them. For example, one of the most important results in quantum physics is the Heisenberg uncertainty principle, which places limits on the precision to which a quantum object’s position and momentum can be determined simultaneously.
Now, by considering the quantum geometric tensor, Koki Shinada and Naoto Nagaosa, both from the RIKEN Center for Emergent Matter Science, have derived constraints for three experimentally measurable parameters of solids.
They also showed how the bounds are analogous to the Heisenberg uncertainty principle. From this, it follows that the bounds they found originate from quantum effects and thus do not apply to classical systems.
This work advances knowledge of both solids and quantum mechanics. “Establishing limits for physical observables is important for deepening our fundamental understanding of the physics of solids,” says Shinada. “Because these limits are closely related to the uncertainty principle, they also have the potential to shed light on the foundational aspects of quantum mechanics itself.”
Shinada considers this is a fruitful avenue for future research. “I believe that viewing the physics of solids through the lens of quantum geometry will be an important future direction,” he says. “A big advantage of this approach is that it yields constraints between different physical observables.”
Shinada suspects that other constructs besides the quantum geometric tensor could be used in a similar manner. “The quantum geometric tensor is only one example of such a quantity; I expect that many other correlations between observables can be uncovered through geometric constraints,” he says. “Ultimately, this approach should deepen our fundamental understanding of the physics of solids.”
Reference
Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
Shinada, K. & Nagaosa, N.
Physical Review B 112 155158 (2025)
RIKEN
