You definitely don't need a CMS.
I'm assuming that your articles are stored (or at least indexed) in a database, and that your index page simply queries that database table to generate the list of article links.
To sort your articles differently, you just need to use different SQL queries - e.g.:
SELECT id, title, author, abstract, date FROM articles ORDER BY title
SELECT id, title, author, abstract, date FROM articles ORDER BY date
SELECT id, title, author, abstract, date FROM articles ORDER BY author
...etc.
So add links to your page that say "Sort by Date" or "Sort by Author" or whatever - or even add a search form, if you want to allow users to search for articles that match specific criteria. Those links will point back to the same page, but with variables in the querystring - e.g., "index.php?sortby=date".
Then, add some PHP code to the page that looks at the querystring, determines which column to order by, and constructs the appropriate SQL query.