It depends on what state you live in, but the laws in most states say that a landlord must give you 24 hours notice to enter your apartment, they must also give you the date and approximate time that they will enter your apartment, they can only enter during normal business hours and they have to have a valid reason to enter (like making that repair). They also have to leave some evidence that they were there if you were not home, like a note or business card.
I would start by calling the property management company's corporate or local office (not your apartment manager, who is probably part of the problem). If it is just a local owner who hired the apartment manager, then insist on talking to the owner. Explain what happened and tell them that you insist on them following the law, that they have to tell you what day and time they will come and they have to come on that day, not another day. Also tell them that your door was left unlocked in the past and you will hold them responsible if this happens again and your apartment is broken into.
Then if they enter your apartment again without following the proper steps, send them a letter via certified mail letting the management company know that they have ignored your request to follow the law regarding entering your apartment and that you have reported them to the local authorities (depending on where you live it could be a city agency or your attorney general). Then report them. They are breaking the law and they need to take you seriously.
Look up your local laws and find out which agency takes care of landlord problems. You can google "landlord/tenant laws + your state" and you should find an official government website (ignore websites that end in .com they are usually wrong). If that doesn't help, look up your local legal aid office they can direct you.