I want to create a P2TR (pay-to-taproot) address but I just want access to the key path spend, I have no use for the script path spend in this specific example. Do I hash an arbitrary string to use as the Merkle root for the script path spend?
BIP 341 (BIP-Taproot) discusses this example where you don't require the script path.
If the spending conditions do not require a script path, the output key should commit to an unspendable script path instead of having no script path.
The BIP also explains here the rationale for this.
If the taproot output key is an aggregate of keys, there is the possibility for a malicious party to add a script path without being noticed by the other parties. This allows to bypass the multiparty policy and to steal the coins.
The Bitcoin Optech workshop on Taproot explains that you calculate the tweaked public key using:
Q = P + H(P|c)G
Q is the tweaked public key P is the initial public key (P = xG where x is the private key) H is the hash function | is concatenation c is the commitment to the script path spend G is the generator point
If you don't need the script path spend you can calculate the tweaked public key using:
Q = P + H(bytes(P))G
bytes(P) is the serialization of P as defined in BIP 340 (BIP-Schnorr).
This tweaked public key Q will be your Taproot (P2TR) address. Remember we don't hash (tweaked) public keys with Taproot (SegWit v1) like we do with P2PKH, P2SH, P2WSH (SegWit v0).