solar sails and outer solar system travel

Recently I came upon the topic of solar sails, and while it's an interesting topic, I find myself having a hard time imaging it being used beyond solar system travel.

To my understanding it uses light to push the space craft, which while amazing seems limited. Yes from earth to mars makes sense, but the moment you leave the solar system the light would be weak, and suddenly there is no more acceleration. Unless you spend forever building up speed in system you're kinda unable to gain any more speed between stars. Am I right?

Or maybe i'm wrong, maybe there is enough light to keep you accelerating between solar system.

Does anyone know how it would work? If Solar sails don't work between solar systems what would work?