  The study of exotic one-dimensional states, particularly those at the edges
of topological materials, demand new experimental probes that can access the
interplay between charge and spin degrees of freedom. One potential approach is
to use a single spin probe, such as a Nitrogen Vacancy center in diamond, which
has recently emerged as a versatile tool to probe nanoscale systems in a
non-invasive fashion. Here we present a theory describing how noise
magnetometry with spin probes can directly address several questions that have
emerged in experimental studies of 1D systems, including those in topological
materials. We show that by controlling the spin degree of freedom of the probe,
it is possible to measure locally and independently local charge and spin
correlations of 1D systems. Visualization of 1D edge states, as well as
sampling correlations with wavevector resolution can be achieved by tuning the
probe-to-sample distance. Furthermore, temperature-dependent measurements of
magnetic noise can clearly delineate the dominant scattering mechanism
(impurities vs. interactions) -- this is of particular relevance to quantum
spin Hall measurements where conductance quantization is not perfect. The
possibility to probe both charge and spin excitations in a wide range of length
scales opens new pathways to bridging the large gap between atomic scale
resolution of scanning probes and global transport measurements.
