Interacting quantum geometry from dressed parametric vertices

Abstract

Quantum geometry has emerged as a powerful framework for understanding topological, optical and transport phenomena, revealing connections between the quantum geometric tensor (QGT) and linear response functions. Building on these developments, recent works formulate quantum geometry so that the parameter space is extended from the Brillouin zone to the space of external perturbing fields that modify the ground state. Here we develop a self-consistent diagrammatric route to determine the QGT for generic parameter spaces, including collective fluctuations or structural distortions. With this in view, we generalize previous approaches to build the geometric tensor from interacting vertex correlations that provide the spectral metric and curvature. The formalism presented here extends the interaction-dressed vertex approach (previously applied to electromagnetic responses in momentum space) to collective electronic and structural deformation fields, complementing ongoing efforts to quantify many-body contributions to quantum geometry.

7 pages, 2 figures