  The Bragg glass phase is a nearly perfect crystal with glassy features
predicted to occur in vortex lattices and charge density wave systems in the
presence of disorder. Detecting it has been challenging despite its sharp
theoretical definition in terms of diverging correlation lengths. Here, we
present evidence supporting a Bragg glass phase in the systematically
disordered charge density wave material PdxErTe3. We do this using
comprehensive x-ray data and a machine learning analysis tool called X-ray
temperature clustering, or X-TEC. We establish a diverging correlation length
in samples with moderate intercalation over a wide temperature range. To enable
this analysis, we introduced a high-throughput measure of inverse correlation
length that we call peak spread. The detection of Bragg glass order and the
resulting phase diagram advance our understanding of the complex interplay
between disorder and fluctuations significantly. Moreover, the use of our
analysis technique to target fluctuations through a high-throughput measure of
peak spread can revolutionize the study of fluctuations in scattering
experiments.
