The rent you are paying your landlord is for "quiet enjoyment". That is, you are paying so that no one can come and tell you that you are trespassing in the place you rent. Your landlord has a duty to take care of the property line issue.
What you should do is write your landlord, if you have not already done so, and let the landlord know about the property line dispute. While the landlord may in fact know about the dispute, you will still need to prove to the court that you follow statutory procedures and notify the landlord by written notice.
If the landlord will not do anything, there in fact may not be anything practical that you can do. While you may sue the landlord for breaching the agreement between you and the landlord, proving damages from not having a few square feet of yard may be difficult.
The written notice to the landlord is to help you to move out once you decide you do not want to live there anymore.
As long as you stay on your side of the fence, the local police likely is not going to do anything about allegations of trespassing. Without a court order regarding the property line, the local police likely would decline to decide where the property line is.
If you decide that you really want to live there, while you have no legal duty to get involved, perhaps you can suggest to the neighbor and the landlord that they, with or without you, go to mediation to work things out.