Yes, they can, but really only in a few instances. The first one is if they have a search warrant to enter and search your home. Law enforcement officers must first knock, announce that they are there, they are law enforcement and they have a warrant. They have to wait a reasonable amount of time for the person to answer the door, but if there is no answer, there is no response, law enforcement officers are allowed to breakdown that door to enter the home and execute the search warrant.
The other instance would be if law enforcement officers are chasing someone who has just committed a crime, a fleeing felon, and the person is running right into a home. There might be certain circumstances where law enforcement officers can run into the home after that person.