Benford's Law Detects Quantum Phase Transitions similarly as Earthquakes

TL;DR

This paper demonstrates that Benford's law, traditionally used to detect anomalies in diverse datasets, can also identify quantum phase transitions in many-body systems by analyzing the distribution of the first significant digit of physical observables.

Contribution

It introduces a novel application of Benford's law to quantum physics, showing its effectiveness in detecting phase transitions in quantum systems.

Findings

Benford's law accurately detects quantum phase transitions.

The method applies to various physical observables.

It offers a simple digit-based detection approach.

Abstract

A century ago, it was predicted that the first significant digit appearing in a data would be nonuniformly distributed, with the number one appearing with the highest frequency. This law goes by the name of Benford's law. It holds for data ranging from infectious disease cases to national greenhouse gas emissions. Quantum phase transitions are cooperative phenomena where qualitative changes occur in many-body systems at zero temperature. We show that the century-old Benford's law can detect quantum phase transitions, much like it detects earthquakes. Therefore, being certainly of very different physical origins, seismic activity and quantum cooperative phenomena may be detected by similar methods. The result has immediate implications in precise measurements in experiments in general, and for realizable quantum computers in particular. It shows that estimation of the first significant digit of measured physical observables is enough to detect the presence of quantum phase transitions in macroscopic systems.