Do PhD students work alone in American universities?
The answer to this question is partly dependent on the field and the dynamics of the research group you are in. I used to work in a spectroscopy lab (in the US) where most of the work was experimental. My impression of the office was that periods of silent concentration were always interrupted by lively discussions, be it scientific or otherwise. We had white boards all over the office and they were never under-utilized. On the other hand, I've also worked in a lab with a more theoretical/computational focuses. There were more international students in the lab, and overall people in the lab were more reserved and largely focused on their own problems. However, I also know of theory labs that have a more lively atmosphere, so I hesitate to say that theory people are more prone to feeling isolated.

I think the solution to your problem is not necessarily moving to a different country. For whatever personal or external reason, collaboration may not be easy for you. But ultimately it is your responsibility to reach out to other people and build collaborations. The easiest targets are people in your research group and your cohort who entered graduate school at the same time. But also consider going to departmental talks and conferences to network with external researchers. As you learn more about your own projects and other people's research interests, it will become easier to start a conversation and explore the possibility of collaborations. It may not come easy to you, but it truly is a necessary training for you as a scientist.