Why would ants unearth pieces of gold? What evolutionary purpose would
this behavior serve?

It makes their chimneys work better.

The workers gather the gold and bring it to the colony. The soldiers use their large powerfull mandibles to shape the soft gold into roughly flat flakes which they distribute around the nest site.

The gold's reflection of the sun's light and heat in an upwards direction has two effects:

• It heats the chimneys, encouraging convection and allowing air circulation around the ant's farmed food source - the fungus below.

_{Attribution BBC 2019}

• It reflects the heat off the surrounding ground, allowing it to be cool - enabling the underground tunnels used for farming the food fungus to expand and grow and thus the colony to be bigger and more succesfull.

_{Attribution: Darwin's Toolkit by UW–Madison CALS 2019}

They don't value the Gold - They expel it from their burrows

What use is a shiny metal to an ant? They don't make artefacts or have currency. They don't have an aesthetic sense apart from food.

The ants line their burrows with a sticky substance they produce from their rear ends. Obviously a lump of gold is an obstruction to the building of their underground kingdoms.

They discard these annoying lumps of useless metal by bringing them to the surface and abandoning them there. If humans remove this refuse then so much the better.

The ants are giant packrats!

The gold digging ants are not typical ants,
http://blogs.getty.edu/iris/the-monstrous-ant-of-the-medieval-bestiary/

There are also ants that, according to some bestiaries, live in
Ethiopia or India, are the size of dogs, and dig up gold from sand,
guard it, and pursue anything that tries to steal it, especially
greedy humans. Artists depicted these ants not as larger versions of
the familiar-looking insects, but more like actual dogs.

http://www.terrierman.com/goldenant.htm

The mountain ant

In ancient Persian the word for marmot was "mountain ant". And the
mountain ants do indeed dig up gold on occasion.

https://www.nytimes.com/1996/11/25/world/himalayas-offer-clue-to-legend-of-gold-digging-ants.html

Now a team of explorers says it has solved the puzzle. The explorers
believe they have pinpointed the land of the legendary gold-digging
ants and the people who profited in one of the most inaccessible
regions of the Himalayas along the upper Indus River.

They say the outsize furry ''ants,'' first described by Herodotus in
the fifth century B.C., are in fact big marmots. These creatures --
Herodotus calls them ''bigger than a fox, though not so big as a dog''
-- are still throwing up gold-bearing soil from deep underground as they dig their burrows. Most important, the explorers say they have
found indigenous people on the same high plateau who say that for
generations they have collected gold dust from the marmots' work.

Here is a colony of these big marmots.

https://www.kathmanduandbeyond.com/feeding-himalayan-marmots-ladakh-india/

But these marmots don't care about the gold. They just bring it up. Why would a rodent care about shiny gold nuggets enough to hoard them and even fight for them? There is one rodent that does. Packrats!

https://nuggetshooter.blog/2018/01/31/pack-rat-gold/

That morning as the horse and mule were loaded Tucker noticed a hole
in his saddlebag with gold dust spilling from it and cussing that rat
for chewing into the bag he began unpacking to save his precious gold,
but it was gone…Only the fine gold that hadn’t spilled from the pouch
into the saddlebag after being chewed apart by the packrat remained.
All of the nuggets were gone as well as his pocket watch, and other
objects small enough for the critter to haul off.

So: your "ants" are colony dwelling, burrowing rodents with a packrat-like habit of hoarding neat things, especially shiny things. In the above linked article, the prospector who lost his gold to the rat spent several days digging into burrows trying to find the one where his gold was, without luck. The article concludes by speculating that in an area naturally rich in gold nuggets, resident packrats might accumulate nuggets over time, giving rise to nugget troves in ancient rodent dens.

I am not sure a marmot would charge a guy with a sword like the ones above are doing but I would not want to test them. They are pretty big one at a time, marmots.

@chasly from UK pointed out that this answer does not cover the evolutionary angle; true. And a downvote for this lack - horrors! I was unable to find any thing written about why packrats might favor shiny things for their nests. I have taken this speculation on myself.

1. Packrats like to incorporate shiny things into their nests - this is well known.




2. Packrats like to use old nests if they can find them. It makes sense - if a nest has long been inhabited that means it is a good place for packrats. Plus older nests are more substantial, in part because of...




3. Amberrat.

https://www.flickr.com/photos/centralaustralia/8419933870

Rats and especially packrats urinate onto their nests. Over time the accumulated urine can crystallize, cementing the nest material together into shiny masses called amberrat. These cemented nests are durable and of use to paleontologists, as the preserved materials record eras past.

Thus we have selective advantage for rats that like old nests, and old rat nests tend to be shiny. This could mean a selective advantage for rats who like shiny nests. Such rats will make their nests shiny if given materials to do so because they like shiny nests. Gold nuggets are definitely shiny. Thus - selective advantage for "ants" that seek out gold and incorporate it into their nest.

Dummy gold war

They are exceptionally clever ants. When they find gold, they plant it on the anthill of they enemy and wait for a human to see it and destroy their enemy.

Very effective.

Sex

First, I'll assume that, as per other answers, we're not actually talking about ants, but rather large(ish) mammals.

Rather than take the packrat route, let's go with bowerbirds. The males build elaborate courtship structures, and decorate them with colorful objects. The satin bowerbird, for instance, is partial to blue.

So, if a species of "ants" has females which are partial to shiny, males will collect and display shiny objects - such as gold nuggets. Furthermore, deep digging which brings up pieces of gold will also be selected for.

It's amazing the number of behaviors which can ultimately be explained by sex.

They live on a planet close to an X-ray star. A layer of heavy metals in their integument gives them some resistance to radiation.

They were engineered this way by a race that lusts for gold. The ants actually eat it, dissolve it in an internal equivalent of Aqua Regia, and plate it out on their integument.

The original species was much less discriminating and would use lead, cadmium, platinum, osmium -- almost any heavy nucleus.

Periodically the engineers land and release a pheromone that brings the ants to collection jars where they are flash burned, and the metal taken for further processing.

Electrical conduction

Gold is a good conductor. Perhaps these ants use electrical pulses (rather than pheromones) to communicate in their nests. So they move the gold so that there are paths wherever they need them. They might also evolve special "router" ants that serve as junctions between paths. So the central pheromone unit (CPU) can send pulses that only reach specific sets of ants. Each ant could be identified by an instead of pheromone (IP) number.

Ants (of any size) communicate largely through pheromones - everything from mating to directions. As it happens, these ants also communicate through pheromones, but something about properties unique to gold either scrambles or removes the pheromone signals. Instinctively realizing that gold, therefore, is quite dangerous, the ants would thus attempt to remove the gold from their burrows, and depending on the strength of the effect, they may even hunt for gold and collect it to keep from being influenced.

Normal ants often have "garbage rooms" where they store their dead, as well as other garbage produced by the hill and its occupants, which would make a fine place to store excavated gold. They may even try to protect this gold, as their instincts have taught them that other creatures can use the gold to disorganize them.

I cant find a good source, but gold found in streams are supposed to be created by bacteria that are allergic to gold. They use mechanisms to make the water stop retaining the gold so it drops to the floor of the riverbed.

Your ants have larvae that are allergic to gold. They might not die from it, but its not good for them. The ants have evolved to actively dig up the gold and drag it to specific area's where larvae will not be living, and the ants who do the digging and dragging will avoid contact with larvae and ants that care for them.

Edit: found source. https://www.businessinsider.com/bacteria-creates-microscopic-gold-nuggets-2013-2?international=true&r=US&IR=T