Benford's law gives better scale exponents in phase transitions of quantum XY models

TL;DR

This paper demonstrates that applying Benford's law to data from quantum XY models improves the detection of phase transitions and critical points, even with low-precision data, outperforming traditional measures.

Contribution

It introduces a novel application of Benford's law to analyze quantum phase transitions, providing better finite-size scaling exponents than existing methods.

Findings

Benford's law accurately detects zero-temperature quantum phase transitions.

The method extends to finite temperature phase transitions.

Analysis is effective even with low-precision experimental data.

Abstract

Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.