Haunt my mind = to think about someone or something all the time Example: You haunt my mind, I can't stop thinking about you because you are so far away. Peace of mind = you feel calm and not stressed out by someone or something Example: Now that we are together again, I have peace of mind.

Haunt means to linger or stay in a place while causing distress. Something which haunts your mind is something which you think about repeatedly and distracts or otherwise distresses you. Peace of mind means you are not distressed by anything. You are calm and your mind is clear. You do not feel fear, stress, or anxiety.