Bedbugs are very difficult to eliminate. Even if your landlord sprays for them, you would need to wash everything washable. And I think you can freeze things or heat them to kill more bugs.

But if the landlord isn't treating the entire building, I suspect the bedbugs will come back.

You might not be able to break your lease, but you might be able to negotiate moving to a different apartment or building, if you rent in a complex. You would then need to treat everything you own to prevent bringing the bugs to the new place.

See if there is a Health Department in your city that you can report the landlord to.

Some states will allow you to put your rent in an escrow account until the problem is resolved. This way, the landlord doesn't get the rent money, but you have shown good faith by paying it into the account. But this depends on the laws where you live.