basement floor crack widening in newly built home - is this a problem?
All NEW buildings move and settle. However, we design them for “uniform” settlement. That is to say, we want the entire building to move together at a specific rate. We don’t want DIFFERENTIAL settlement. 

Differential settlement can occur from one portion of a building moving up, down or sideways differently than another portion. 

It’s always a result of bad planning. I live where the ground is mush, but we plan for it and provide larger footings, piers or piling and thus have no problems. However, when we build over a “soft spot” that we didn’t account for, one portion of the building will settle more than another and we have problems. When this happens, slabs or footings will always “step” apart.

Your pictures show the slab “level”, so you do not appear to have any of these conditions. 

However, EXCESSIVE movement caused by excessive amount of water in the concrete mix is more common and appears to be your problem. 

There is an exact amount of water to be used (mixed) with Portland Cement to give it it’s ideal working consistency and strength. We call this it’s water/cement ratio. 

However, it’s tempting for workmen to add additional water to the recommended mix design so that it is easier to “work” the concrete before it “sets”.

However, when this is done, then more water causes greater shrinkage when the concrete dries (cures). Your concrete must have been very “wet” because there is an extremely large “shrinkage” crack now. In fact, now the tile has cracked where the slab has shrunk and cracked. 

When we get involved in fixing these types of cracks we monitor the crack to make sure it has stopped moving before we fix the problem. 

I’d recommend that you tape a plastic ruler to one side of the crack, install a box over the ruler so it can’t be moved, and then create a photo journal taking pictures each month for 1 year and writing down observations: like width of crack, outside temperature, room temperature and humidity. Usually after 1 year you’ll know if it’s stopped moving. (That is to say, you’ll know if the slab has stopped shrinking.)

Then, to repair the problem, I’d add a tile “expansion joint” directly over the crack. 

Because the concrete crack is irregular, the two slabs will probably not move up or down causing differential settlement. Just make sure the slab has stopped shrinking. It may take up to a year.