Emergent Distance and Metricity of Mutual Information in 1D Quantum Chains

2025/07/13 by Leighton-Trudel, Beau
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2507.09749

Abstract

We develop and formalize a phase diagnostic based on the information-distance \(d_E = K₀/√(I)\) (mutual information \(I\)) for 1D quantum chains. Calibrating with the Euclidean benchmark \(I(r)∝ r^-2↦ d_E(r)∝ r\) makes the triangle-inequality test parameter-free and scale-invariant. Under site-averaged, monotone scaling conditions on the 1D line we establish a criterion linking the decay of \(I(r)\) to metric behavior of \(d_E(r)\): power laws \(I(r)∼ r^-X\) with \(0

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