how can i leave a field without value if the condiction is true?

Question

for(Account acc : lstAc){
    Account acount =  new Account(); 
    if (acc.Property_Managment_Company__c == 'Independent') {
               acount.ParentId =  THIS FIELD SHOULD BE EMPTY.
            }
        }       

Answer 1

Since you don't describe the use case here, I'd suggest this as a validation rule on the Account object to prevent the data from being set incorrectly in the first place.

Formula:

AND (
  Property_Managment_Company__c = 'Independent',
  NOT(ISBLANK(ParentId))
)

Error Message:

This account is independently managed and cannot have a parent account specified

If this field value is being changed in code, as others have suggested, ParentId = null will do the job of erasing the parent reference.

Answer 2

I am not sure why you are creating new instance of Account object inside for loop. But you can try following code:

for(Account acc : lstAc){
     if (acc.Property_Managment_Company__c == 'Independent') {
          acc .ParentId =  null;
     }
  } 
update lstAc;