Effects of the Hubbard interaction on the quantum metric

TL;DR

This paper investigates how repulsive Hubbard interactions affect the quantum metric in quantum systems, showing that interactions suppress the metric and proposing improved theoretical definitions validated by exact diagonalization.

Contribution

It introduces and compares the generalized and dressed quantum metric definitions in the context of interacting systems, demonstrating the dressed metric's superior accuracy.

Findings

Hubbard interactions monotonically suppress the quantum metric.

The dressed quantum metric aligns better with exact diagonalization results.

The conclusions apply to both flat-band and dispersive systems.

Abstract

Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting weight, Drude weight, and optical responses. Motivated by the recent advances in flat-band interacting systems, we investigate the role of interaction effects on the quantum metric. By using the fermionic Creutz ladder as a representative system, we show that the repulsive Hubbard interaction monotonically suppresses the quantum metric. While the eigenstates and their overlap quantifying the quantum metric can be obtained exactly in the presence of interactions through exact diagonalization, this method is limited to small system sizes. Alternatively, two theoretical proposals, the generalized quantum metric and the dressed quantum metric, suggest using renormalized Green's functions to define the interacting quantum metric. By comparing these analytical approaches with results from exact diagonalization, we show that the dressed quantum metric provides a better fit to the exact diagonalization results. Our conclusion holds for both flat-band and dispersive systems.