In Corollary 4.6 of this paper https://core.ac.uk/download/pdf/81991766.pdf they seem use a result that if $\Delta : D \to H$ is essentially self adjoint, such that $D \subseteq H$ is a dense subset of a Hilbert space $H$, with $(I - \Delta)^{is}: H \to H$, defined by some spectral theory, bounded then $$ [X^s, X^r]_t = X^{tr + (1-t)s} $$ where $X^s = (I - \Delta)^{-\frac s2}H$ and $[\cdot,\cdot]_t$ denotes complex interpolation.
I think this is a fairly standard result from interpolation / spectral theory, but I can't find any references for this. Is this statement true, and are there any references describing this?