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

## TL;DR

This paper reveals a universal quantum phase transition in Lifshitz scalar systems, shifting from continuous to discrete scale invariance at a critical interaction strength, highlighting a fundamental change in symmetry behavior.

## Contribution

It introduces a universal transition in Lifshitz scalar models, connecting continuous and discrete scale invariance, and characterizes the critical coupling for this phase change.

## Key findings

- Existence of a universal transition between scale invariance phases
- Identification of a critical coupling for the phase transition
- Demonstration of discrete scale invariance emergence

## 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 $\lambda_{c}$ corresponding to a strongly attractive potential.