The 8th United States was the only regiment of Regular infantry in the Army of the Potomac not attached to the Division of Regulars in the Fifth Corps. It was assigned to Army Headquarters as Provost Guard.
From the monument:
Army of the Potomac
Headquarters, Provost Guard
Eighth U.S. Infantry
Captain Edwin W.H. Read commanding
July 2 Arrived in the morning and engaged in provost duty until the close of battle.
See more on the 8th United States Infantry in the Civil War