Applying to PhD programs while pursuing a PhD Imagine the following situation. Somebody is doing their PhD in field A in the US. 
 Suppose they became interested in a different field, field B, and consider doing PhD in field B instead. Suppose further that the university they are doing PhD at is not suitable for doing PhD in field B for some reason. Is it acceptable to apply for PhD positions in field B in other universities without notifying their current university until after they have been admitted to a program of their interest? The reason for doing this is to ensure that if they don't get accepted anywhere, then they could just continue pursuing their PhD in field A (which is also an acceptable option for them).
In most fields in the US this would be acceptable. An exception might be if you have accepted a grant that has some sort of termination clause that prevents it or makes it difficult. If you wind up leaving your current position you might have some ethical obligation to finish up some tasks if they affect others, but that is a separate question. 

In general, though, you can seek a better position for yourself. 

But you will also need to be able to explain to the new institution why you are leaving and why you are a good prospect for their program. Self awareness and learning are usually a good reason that (most) people will accept.