If a single private key of the HD bitcoin account is compromised, is the whole HD account compromised?
With just the private key, no.

However, if the attacker knows both a child private key and the xpub of the chain it is derived from, yes.

From BIP32:


  One weakness that may not be immediately obvious, is that knowledge of a parent extended public key plus any non-hardened private key descending from it is equivalent to knowing the parent extended private key (and thus every private and public key descending from it). This means that extended public keys must be treated more carefully than regular public keys. It is also the reason for the existence of hardened keys, and why they are used for the account level in the tree. This way, a leak of account-specific (or below) private key never risks compromising the master or other accounts. 


This means you should either never give out private keys, or treat xpubs are highly sensitive secret data.

When using hardened derivation, this problem doesn't exist, but they lack the ability to publicly derive addresses.