A lot of answers here asking if just leaving is unprofessional, but none state this fact you state bluntly at the opening of your question here:
“I started my job 2 months ago…”
Okay, so it is indeed unprofessional to leave 1 week into a 2 week notice period. That said, here is the question that I will ask you:
Does a job you have barely been at 2 months actually matter in the long run?
Do you plan on using this place as a reference? Do you forfeit pay or something else that is tangible by just leaving? If the answer to these questions are “No…” my advice is you should just leave and clearly state why:
- Boss is Acting Unprofessional: You tried to be nice about leaving, but your boss is making your life in the office miserable.
- Nothing to Do: You literally have nothing to do but be physically present and don’t feel that is right.
In my humble opinion, if you were there for — let’s say — three months or longer, perhaps you should stick it out for the full 2 weeks.
But if you have only been there 2 months and you don’t plan on using the employer as a reference or have another professional reason for staying, just leave.
The note you should leave with HR should not be nasty or vindictive. It should be honest and and productive towards the company. Something like:
“Look, I have only been here 2 months, gave 2 weeks notice, but my boss has been making the last week miserable. Since I have only been here for 2 months, I don’t feel obligated to endure another week of this treatment.”
You are not burning a bridge by just ditching a job you had so little roots in; you are simply stating: “This is not working out…”
And for perspective, 20-ish years ago many employers would only consider a “new employee” truly a part of the team after a full 3 months. After 3 months many places would then offer you things like health insurance and such because many employers know people don’t really know how they would fit into a workplace after those first 3 months.
My advice? Move on. Make it easier for all sides.