I wonder if I have previously installed ubuntu with root, home, and swap partition. And now I want to change distro to arch linux. Is it so that I only need to wipe my root-partition and install arch linux there instead?
You can safely leave the swap partition as is, it can be shared among different distros. The root partition definitely has to be wiped, as you expect.
The home partition is somewhere in the middle. Of course your data and settings will not harm the new installation, but a difference in configuration options may give you weird errors.
A better approach is to back up the home partition somewhere, then install the new distro (wiping the home partition on the way). When you are done with installing the new distro, simply recover from the backup.
Or, if you don't like backups, just cross your finger and install it that way, keeping the home partition. In the case of errors, try creating a new user to check. If the new user does not have the problem then you know you have to clean up your configurations :) I don't like this approach because it's less clean. Arch and Ubuntu are so different that I'm quite sure there will be lots of unused dot files in your home directory.
that should do as far as i know, but it may also effect some dependancies whose effects may not be immediately visible