Let me start out by saying that you have a very original concept; one that I haven't ever really seen before. However, I think a bit more backstory is needed as to why the wizards are living underground. You mentioned the strict Muggle government, but I think that elaboration would have been good. You say that being different isn't good, but there is never really a reason behind why it is bad, why the government doesn't want variation.

The transition between the first and second paragraph is a bit awkward. Perhaps you should add something like asteriks in between to make it flow more smoothly and indicate a change of speaker better.

In the fourth paragraph, you day that Lexi hears footsteps on the roof of her house, and that confused me a bit. For one, I believed that her home was underground, and that the roof was made of earth. Also, though, it seems as if she solves the problem of the footsteps on the roof by encountering her parents in the kitchen, which didn't really seem to have anything to do with the roof.

I like the way you gave Lexi the talent of drawing, it adds a lot to her character. The way she sees it as an escape is also a good description.

A few paragraphs downs, Lexi is running towards the marketplace, following the footsteps again. I thought that she stopped looking for their source when she overheard her parents in the kitchen.

Nice backstory on the man with the guitar; it leaves the reader wanting more.

Anyways, very original story and keep up the good work!

very interesting first chapter, i'm looking forward to reading more.