To perform archive actions related to a Content Document in public and private libraries, the authenticated user must have the following permissions:
Archive
Query All Files
Unarchive
Set Audit Fields upon Record Creation
Update Records with Inactive Owners
#1 requires enabling the organization level via: Setup, User Interface, Enable “Set Audit Fields Upon Record Creation” and “Update Records with Inactive Owners” User Permission.
For additional permissions requirements, see here.