Archive Tree
The Archive Tree is an append-only Merkle tree that stores the Headers (see the diagram below) of all previous blocks in the chain as its leaves.
For most chains this is not required since they are always executing at the head of the chain. However, private execution relies on proofs generated by the user, and since users don't know the current head they must base their proofs on historical state. By including all prior headers (which include commitments to the state) the Archive Tree allows us to easily prove that the historic state that a transaction was proven upon is valid.
Furthermore, since each Header includes a snapshot of the Archive Tree as at the time of insertion, as well as commitments to the Header's block content and global variables, we can use the Archive Tree to prove statements about the state at any given block or even transactions that occurred at specific blocks.