Scale anomaly of a Lifshitz scalar: a universal quantum phase transition to discrete scale invariance

Abstract

We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time. These systems describe a Lifshitz scalar interacting with a background potential. The transition occurs at a critical coupling $λ_{c}$ corresponding to a strongly attractive potential.

6 pages, 3 figures + 3 pages supplementary material; v2: minor typos corrected, additional text of published version added