I have one non-privileged account on a Linux server and I don't want root to read my documents.
How do I find out if root did something I don't want to happen?
This issue is not the same as Super users and the home directory.
There is no way to prevent the root user from being able to read or write documents for an unprivileged account. Even more so, the root user can change the permissions of those documents. The whole point of having such a user is that you always want to be able to have no restrictions when it comes to maintaining a system. That's why the root user should not be used for daily tasks.
Furthermore, even if there were access logs to files, that would probably be controlled by root again. Also, the atime (last access time) isn't reliable for this, or might not even be recorded on your system. You'd have to be able to check the shell history of the root user, which, again, is not possible without a privileged account.
The only way to make your files safe from prying sysadmin eyes is to encrypt them, e.g. by putting them into a TrueCrypt container or using GnuPG.