Not so simple

http://www.nolo.com/legal-encyclopedia/free-books/renters-rights-book/chapter9-5.html

in most states landlords cannot simply sit back and wait for the term to end, then sue you for the months you weren’t there. They must take reasonable steps to rerent the place and credit that rent to your debt. This duty goes by a mouthful of words—“the landlord’s duty to mitigate damages.