Schizophrenic Neighbor

I'll try to keep this short and spare you some of the details, but basically my girlfriend are being harassed by our neighbor and we're wondering if there's any legal recourse we can take.

We just graduated college and moved into our first apartment together. We have a neighbor that lives across the parking lot from us and can see us if we are out on our balcony, walking to our car, etc.

I won't go into every incident, but he has extremely erratic and concerning behavior. And whenever he sees us, he yells profane verbal threats and insults.

We also witnessed him being arrested (I assume) as we saw him escorted by police in handcuffs and taken from his unit into a cop car. However we saw him back home not too long after that.

I recently had my first (and only) interaction with him: he came into the apartment gym while I was working out, and he immediately got in my face and started cussing me out for no reason. I could tell right away that he must have some severe mental impairment. I was able to de-escalate the situation and leave before it got physical, and he was certainly pushing it in that direction.

Long story short - we are now aware he has schizophrenia, and so is management. I'm not sure how functional he is, if he's on medication, or how well he can take care of himself... but I know that he lives alone, and something about that just doesn't seem right to me.

He has yelled offensive and crude comment towards my girlfriend, and she is now too scared to go outside. She can't even go on a walk or read outside because this person's behavior is so unpredictable that it scares her.

We have told management everything, and apparently there's nothing they can do, since he hasn't technically violated the terms of the lease.

Management has sucked from day one, from lack of communication, to making up rules that aren't on the lease agreement. It's a brand new apartment complex and it's clearly the property managers first rodeo.

Details that may be important:

1. my employer rents this apartment out for us in their name. I work in construction, and must stay here until the project is complete.
2. although the neighbor has yelled profane insults at us, I'm not sure anything would count as sexual harassment or any real criminal offense.

I'm just sick of my girlfriend not feeling safe in her own home, and not being able to use the apartment amenities. I'm not sure what options I have in this scenario but any advice would be greatly appreciated!

Location: North Augusta, SC