  The geometric characteristics of Bloch wave functions play a crucial role in
electronic transport properties. We show that the thermoelectric performance of
materials is governed by the geometric structure of Bloch wave functions within
the framework of the Boltzmann equation. The essential geometric notion is the
Hilbert-Schmidt quantum distance, measuring the resemblance between two quantum
states. We establish a geometric characterization of the scattering rate by
extending the concept of quantum distance between two states in momentum space
at a distance.Employing isotropic quadratic band touching semimetals, where one
can concentrate on the role of quantum geometric effects other than the Berry
curvature, we find that the response functions for electrical quantum transport
and, therefore, the thermoelectric power factor can be succinctly expressed in
terms of the maximum quantum distance, $d_\mathrm{max}$. Specifically, when
$d_\mathrm{max}$ reaches one, the power factor doubles compared to the case
with trivial geometry ($d_\mathrm{max}=0$). Our finding highlights the
significance of quantum geometry in improving the performance of thermoelectric
devices.
