Can I keep the security deposit if the tenant move out before lease ends?

[James Qiu]

I have a tenant who's moving out early. However he signed the lease to next March. So legally he is responsible for the remainder of the lease. The lease which is a standard CA rental lease also says the Landlord may withhold lost Rent from the security deposit. So does what mean I can legally keep all his deposit? If I can fill the rental quickly, do I need to refund the remaining depsoit after subtracting lost rent, cleaning, and other costs?

I'm pretty new at this, so any suggestions are appreciated.