is there a CA law that requires mandatory carpet cleaning to be paid by the landlord if the tenant leases for over a year, once a year?
No. Please see pp. 59-60 of the guide linked below.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.