Do whatever feels right for you. There's no right or wrong answer, it depends on the people. After a first date with one of my past boyfriends we didn't talk at all until our second date, except to clarify that we'd be meeting each other. And that suited us and worked. With my current boyfriend between our first and second dates, which had about a week in between, we stayed up until 4am messaging each other almost every night. And that suited us and worked.

So it just depends on how you feel.