  A simple example is used to show that renormalization group limit cycles of
effective quantum theories can be studied in a new way. The method is based on
the similarity renormalization group procedure for Hamiltonians. The example
contains a logarithmic ultraviolet divergence that is generated by both real
and imaginary parts of the Hamiltonian matrix elements. Discussion of the
example includes a connection between asymptotic freedom with one scale of
bound states and the limit cycle with an entire hierarchy of bound states.
