2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201432A 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.8 pages, 3 figures, revtex4High Energy Physics - Theorytext