At the Wikipedia article on time complexity, only a PRAM example is given for polylogarithmic time.
Let $T(n)$ denote the largest number of steps used by a machine to reach a final state on any input with size $n$ bits.
Is there a program for a standard sequential model of computation (e.g. a Turing machine or a sequential random-access machine), solving some natural problem, so that $T(n) \in \Theta((\log n)^k)$ for some fixed $k>1$?