How can I convey my knowledge about a field without publications in a PhD application?
Given that you're a sophomore at a fairly selective liberal arts college [*], you still have plenty of time. Indeed, in two years time the work you're doing now might seem rather simplistic and quaint to you, due to your likely much greater "maturity" in relevant subject-matter knowledge by then.


[*] You mentioned this in a comment. You should probably include this information in your question, but perhaps omit the name of the college.


I recommend considering doing a more advanced independent study course with an appropriate faculty member, impress the faculty member, and ask this faculty member be one of those who will write a letter of recommendation for you when you apply to graduate programs. And also do what @Dan Romik suggests.