Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator

TL;DR

This study uses information theory to analyze how quantum and classical correlations develop in a doped Mott insulator's superconducting state, revealing entropy suppression and correlation amplification across doping levels.

Contribution

It introduces an information-theoretic approach to characterize superconductivity in a doped Mott insulator, linking entropy and mutual information to the superconducting transition.

Findings

Local entropy detects superconductivity and correlates with potential energy changes.

Superconducting state suppresses thermodynamic entropy, decreasing with doping.

Mutual information is enhanced in the superconducting state across all doping levels.

Abstract

A key open issue in condensed matter physics is how quantum and classical correlations emerge in an unconventional superconductor from the underlying normal state. We study this problem in a doped Mott insulator with information theory tools on the two-dimensional Hubbard model at finite temperature with cluster dynamical mean-field theory. We find that the local entropy detects the superconducting state and that the difference in the local entropy between the superconducting and normal states follows the same difference in the potential energy. We find that the thermodynamic entropy is suppressed in the superconducting state and monotonically decreases with decreasing doping. The maximum in entropy found in the normal state above the overdoped region of the superconducting dome is obliterated by superconductivity. The total mutual information, which quantifies quantum and classical correlations, is amplified in the superconducting state of the doped Mott insulator for all doping levels, and shows a broad peak versus doping, as a result of competing quantum and classical effects.