  When the scattering length is proportional to the distance from the center of
the system, two particles are shown to be trapped about the center.
Furthermore, their spectrum exhibits discrete scale invariance, whose scale
factor is controlled by the slope of the scattering length. While this
resembles the Efimov effect, our system has a number of advantages when
realized with ultracold atoms. We also elucidate how the emergent discrete
scaling symmetry is violated for more than two bosons, which may shed new light
on Efimov physics. Our system thus serves as a tunable model system to
investigate universal physics involving scale invariance, quantum anomaly, and
renormalization group limit cycle, which are important in a broad range of
quantum physics.
