Essay: Where Can Quantum Geometry Lead Us?
- URL: http://arxiv.org/abs/2312.11516v1
- Date: Tue, 12 Dec 2023 19:03:59 GMT
- Title: Essay: Where Can Quantum Geometry Lead Us?
- Authors: Paivi Torma
- Abstract summary: Quantum geometry defines the phase and amplitude distances between quantum states.
Various quantum transport and interaction phenomena have been found to be critically influenced by quantum geometry.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum geometry defines the phase and amplitude distances between quantum
states. The phase distance is characterized by the Berry curvature and thus
relates to topological phenomena. The significance of the full quantum
geometry, including the amplitude distance characterized by the quantum metric,
has started to receive attention in the last few years. Various quantum
transport and interaction phenomena have been found to be critically influenced
by quantum geometry. For example, quantum geometry allows counterintuitive flow
of supercurrent in a flat band where single electrons are immobile. In this
Essay, I will discuss my view of the important open problems and future
applications of this research topic and will try to inspire the reader to come
up with further ideas. At its best, quantum geometry can open a new chapter in
band theory and lead to breakthroughs as transformative as room-temperature
superconductivity. However, first, more experiments directly showing the effect
of quantum geometry are needed. We also have to integrate quantum geometry
analysis in our most advanced numerical methods. Further, the ramifications of
quantum geometry should be studied in a wider range, including electric and
electromagnetic responses and interaction phenomena in free- and
correlated-electron materials, bosonic systems, optics, and other fields.
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