Quantum Geometric Advantage of the Correlated Exciton State in Non-linear Optics

TL;DR

This paper reveals that the quantum geometry of correlated exciton states significantly influences non-linear optical responses, providing a new perspective on many-body effects in condensed matter physics.

Contribution

It introduces the concept of quantum geometry for interacting electron-hole pairs and demonstrates its impact on non-linear optics through first-principles calculations.

Findings

Quantum many-body geometry enhances non-linear optical responses.

The many-body shift vector acts as an analogue of the Berry phase.

Correlated exciton states' geometry plays a crucial role in optical properties.

Abstract

The concept of quantum geometry for single-particle states has revolutionized our interpretation of several emergent properties in condensed matter. However, a description of the quantum geometry for interacting particles and an understanding of its implications are lacking. Here, we show that inherent in the non-linear optical response is a quantum geometry of the correlated electron-hole state (exciton) that arises from the interplay between geometry and interactions - distinct from the quantum geometric properties of the individual electron or hole states. We demonstrate using first principles calculations that this quantum many-body geometry significantly enhances the non-linear optical response in systems with strong excitonic effects. In the case of shift currents, the quantum many-body geometric term arises in the many-body shift vector and can be interpreted as a many-body analogue of the Berry phase. This work lays the foundation to study the quantum geometry of correlated states in experimentally observable settings.