Tenant Wants to Break Lease; What is "re-rent levy"

[John Mark]

Hello,
We have tenants that signed a 2yr lease to rent our home in the state of NM. The tenants want to break the lease and move out after only being in the home for 3 months. Our understanding is that in NM, the tenant is on the hook for the entire term of the lease, whether the home is occupied or not, but the landlord needs to take steps to get it re-rented as soon as possible. 

Our lease spells out a "re-rent levy" of 3 months rent for breaking the lease. Is the "re-rent levy" suppose to release the tenant from the contract or do they have to pay the "re-rent levy" in conjunction with the monthly rent still owed under the contract and until either the lease expires, or we re-lease the property? Also, if the tenant is still on the hook for the lease until it is rented again, are they required to continue providing/paying for basic utilities and lawn maintenance or is this what the "re-rent levy" is for? Thanks!