I think, No a landlord can't enter your apartment, without your consent. That is not illegal for him to do.
If you have paid rent rent and you r living in it then landlord cannot come there into the apartment he has no right to do so.And should inform you in advance if there is any emergency suituation.
The rights of landlords vary from state to state. Some states are landlord friendly; some are tenant friendly.
What is legal in Main (for example) may or may not be legal in Nevada (for example).
I see a lot of answers come from people who consider such an action an "invasion or privacy" or against some other principle or valid reason for concern.
Unless you have studied real estate specifically, you do not know whether real estate law and your specific lease contract apply those principles in the same way.
Here's a site that will give you an overview of the considerations involved in answering your type of question.