I have read An Introduction to the Intel® QuickPath Interconnect. The document does not mention that QPI is used by processors to access memory. So I think that processors don't access memory through QPI.
Is my understanding correct?
Yes, QPI is used to access all remote memory on multi-socket systems, and much of its design and performance is intended to support such access in a reasonable fashion (i.e., with latency and bandwidth not too much worse than local access).
Basically, most x86 multi-socket systems are lightly1 NUMA: every DRAM bank is attached to a the memory controller of a particular socket: this memory is then local memory for that socket, while the remaining memory (attached to some other socket) is remote memory. All access to remote memory goes over the QPI links, and on many systems2 that is fully half of all memory access and more.
So QPI is designed to be low latency and high bandwidth to make such access still perform well. Furthermore, aside from pure memory access, QPI is the link through which the cache coherence between sockets occurs, e.g., notifying the other socket of invalidations, lines which have transitioned into the shared state, etc.
1 That is, the NUMA factor is fairly low, typically less than 2 for latency and bandwidth.
2 E.g., with NUMA interleave mode on, and 4 sockets, 75% of your access is remote.