Until recently this was the only Tennessee monument on the battle field. It is for Bate's 2nd Tennessee Infantry, there actually were two 2nd Tennessee Infantry regiments at Shiloh (Bate's and Walker's). It is near Shiloh Church.
There are two oddities to this monument that I've always had a hard time understanding. The first is that it quotes General Cleburne's report concerning what the regiment did, "Tennessee can never mourn for a nobler band than fell this day in her second regiment." But it misspells Cleburne as Cleburn. Surely by the time this monument was erected they had to know how to spell his name, he was not a hero or household name at the time of Shiloh but after the war he was much more of a household name, but apparently not enough to get his name spelled right.
The other oddity is the flag on the monument. I've researched it a bit and as far as I can tell this style was not in circulation at the time. Perhaps it is a model of the 2nd Tennessee's flag, I've never seen a copy of the flag they carried at Shiloh. What it looks like is the modern Mississippi state flag but why that would appear on a Tennessee monument is even more confusing. My best guess is that is what Bate's 2nd Tennessee carried but maybe a flag expert out there can better enlighten us all.