Renormalization Group Limit Cycles in Quantum Mechanical Problems

Abstract

We formulate a renormalization group (RG) for the interaction parameters of the general two-body problem and show how a limit cycle emerges in the RG flow if the interaction approaches an inverse square law. This limit cycle generates a scaling structure in the energy spectrum. Our demonstration is relevant to the Efimov problem in nuclear physics where similar scaling appears.

5 pages, 2 figures (1 BW, 1 color), RevTeX4; ver2: updated references; Due to strong overlap with [Kolomeisky and Straley, Phys. Rev. B 46, 12664 (1992)] this paper is no longer being considered for publication