Drude weight and the many-body quantum metric in one-dimensional Bose systems

TL;DR

This paper explores how quantum geometry influences the transport properties of one-dimensional interacting bosonic systems, revealing that the many-body quantum metric bounds the Drude weight, with validation on a flat band model.

Contribution

It introduces a relationship between the Drude weight and the many-body quantum metric, highlighting the metric's role in determining the upper bound of conductivity in such systems.

Findings

Drude weight equals kinetic energy plus a quantum metric term

Many-body quantum metric bounds the Drude weight

Validation performed on the Creutz ladder model

Abstract

We study the effect of quantum geometry on the many-body ground state of one-dimensional interacting bosonic systems. We find that the Drude weight is given by the sum of the kinetic energy and a term proportional to the many-body quantum metric of the ground state. Notably, the many-body quantum metric determines the upper bound of the Drude weight. We validate our results on the Creutz ladder, a flat band model, using exact diagonalization at half and unit densities. Our work sheds light on the importance of the many-body quantum geometry in one-dimensional interacting bosonic systems.