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

摘要

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.