Observing Golden Mean Universality Class in the Scaling of Thermal Transport

TL;DR

This paper investigates the universality class of thermal transport scaling, revealing the golden mean exponent in a quartic anharmonic chain and discussing phase transitions affecting the universality class.

Contribution

It provides the first precise estimate of the golden mean as the scaling exponent in a specific anharmonic chain and explores how cubic anharmonicity influences the universality class.

Findings

Golden mean exponent observed in quartic anharmonic chain

Inclusion of cubic anharmonicity shifts the universality class to gamma=5/3

Phase transitions alter the symmetry and dynamic structure factor, affecting scaling exponents

Abstract

We address the issue of whether the golden mean $\left[\psi=(\sqrt{5}+1)/2 \simeq 1.618\right]$ universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show estimate with unprecedented precision, that $\psi$ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems somewhat deviation from the previous expectation and we explain it by the unusual slow decay of the cross-correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross-correlation is gradually died out and another universality class with scaling exponent $\gamma=5/3$, as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to $\gamma \simeq 1.580$ emerges. All these evidences suggest that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.