What is the smell after quartz is rubbed together? When I rub quartz together, it glows due to triboluminescence but it also creates a burnt smell. What causes that smell?
 A: A good question that has long been asked, as shown by a 1900 Nature letter  inquiring about The Smell emitted by Quartz when Rubbed.
Rubbed quartz can produce more than one smell, so this is an extension of the original answer in light of comments from others and new information from the original poster that the smell is not specific to triboluminescent quartz.
As noted in the answer to Milky quartz stones give off odour after being struck - persistent tribo-odorosity(?), an odour from rubbed quartz could be due to the release of hydrogen sulfide (H2S) trapped in tiny inclusions in the quartz.  When you rub together two pieces of quartz, you break open some of the microscopic inclusions and release the hydrogen sulphide.
As @akhmeteli's answer citing an 1858 Scientific American article shows, the basics of this have long been known, but the details have been more recently confirmed. The presence of hydrogen sulfide in inclusions has been noted by studies such as this 1984 article on "Gas chromatographic analysis of volatiles in fluid and gas inclusions" which reported that hydrogen sulfide was the dominant gas released when a sample of "fetid quartz" was crushed. Another study the same year reported on Characterization of H2S bearing fluid inclusions in quartz, fluorite, and calcite.
As correctly noted in @user346760's answer and @kryan's comment, the question describes the smell as "burnt", not the usual "rotten egg" description of low concentrations of hydrogen sulfide.
The 1858 cited Scientific American article mentions a rotten egg smell, but Thomas Wedgwood described it simply as "strong" in a 1791 Royal Society report,  Delius referred to it as "sulphurous" in 1748, and other common descriptions include "metallic".
If the smell is "burnt" and not "rotten eggs", then also as noted by @user346760, the triboluminscence could be igniting contents of the inclusions.  Hydrogen sulfide is a volatile flammable gas which burns to sulphur dioxide and water.  Sulphur dioxide is a pungent gas which causes the smell of burnt matches. It is also possible that any elemental sulphur inclusions could be ignited producing sulphur dioxide, but such inclusions seem to be less frequently mentioned than H$_2$S inclusions in the scientific literature.
As noted by @KRyan, it is also possible other compounds could contribute to the smell. The most common other volatile components of quartz inclusions are odorless, i.e. water, methane, and carbon dioxide, but the surface of a quartz pebble could absorb organic materials from its environment.
Although I believe all the above discussion is accurate, it may be moot in light of new helpful information from the original poster that the same smell is produced when two random rocks are rubbed together. Both the original poster and myself have confirmed that the same smell is produced by rubbing together a variety of rocks and even from simply vigorously rubbing two glass jars together, but not when metal or plastics are rubbed together. Since the smell can be produced by rubbing glass together, this is clearly not a sulphur related smell due to inclusions.  Personally, the smell makes me think of electric motors, e.g. ozone. Others with more sensitive and experienced noses may be able to identify it better.
That ozone may be significant component of the smell is certainly plausible.  Ozone is produced when granite blocks are crushed or when grinding granite, basalt, schist, rhyolite, or gneiss. If ozone is being produced, then as noted in the answer to Where does the smell of electrostatic charge come from?, we can also expect nitrogen oxides. This is similar (but on a much smaller scale) to gas production by of lightning.
The smell of ozone has been variously described as "chlorine, metal, burnt wire"
Nitrogen oxide is a "sharp sweet-smelling gas" and nitrogen dioxide has "a strong, harsh odor".
It seems likely that the general smell of rubbing rocks (or glass) together is mostly due to some combination of these.
A: It is the smell of sulfur dioxide gas ($\text{SO}_2$) being released, as the elemental sulfur inclusions are getting oxidized in the air due to the heat caused by friction.
It is NOT, as all the other replies assume, hydrogen sulfide. A quick check of the properties of those two gases confirms that it could not have been $\text{H}_2\text{S}_{}$, as it has the pungent and foul odor of rotten eggs. Meanwhile, sulfur dioxide has the smell of just-struck match, or burnt fireworks.
A: For what it's worth:

When certain varieties of quartz and limestone are strongly rubbed,
they give off the odor of rotton eggs. This peculiar smell is
occasioned by the evolution of sulphureted hydrogen

I guess "sulphureted hydrogen" is the same as hydrogen sulfide.
