Benford's Law Detects Quantum Phase Transitions similarly as Earthquakes

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.

v1: 3 pages, 2 figures; v2: 6 (+epsilon) epl pages, 5 figures, significant additions, previous results unchanged

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Quantum computing with trapped ions
• 14-qubit entanglement: creation and coherence
• Multipartite entanglement in spin chains
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Quantum discord in finite XY chains
• The low-$T$ phase diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Thermal robustness of multipartite entanglement of the 1-D spin 1/2 XY model

Cited by in corpus (9)

• Quantum discord and its allies: a review
• Benford's Law and the Universe
• Regularities and Discrepancies of Credit Default Swaps: a Data Science approach through Benford's Law
• Using skewness and the first-digit phenomenon to identify dynamical transitions in cardiac models
• Benford's distribution in extrasolar world: Do the exoplanets follow Benford's distribution?
• Benford's law gives better scale exponents in phase transitions of quantum XY models
• Benford Analysis: A useful paradigm for spectroscopic analysis
• Statistics of leading digits leads to unification of quantum correlations
• Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better