Mizmor shir l'yom haShabbat, tov l'hodot laHaShem.The opening phrase of the special chapter of Tehillim for Shabbat: a song for Shabbath, it is good to thank HaShem.
This is all seems rather arcane, just like all the rest of the teachings of Rebbe Nachman, but just like all the other teachings of Rebbe Nachman, it's really so simple.
Why is saying thank you the defining characteristic of Shabbat? From a purely Halachic sense, we can't ask for anything on Shabbat, it is forebidden -- the only kind of prayer available to us? Saying thanks!!
From a slightly more idyllic place: Shabbath is the day we sit back and let HaShem provide for us. Since He's providing for us, it's only appropriate that we say, "Thank you!"