Slow melting of a disordered quantum crystal

TL;DR

This paper investigates how quenched disorder affects the melting dynamics of a quantum crystal, revealing a slowdown from ballistic to logarithmic erosion without inducing many-body localization, supported by perturbative and numerical methods.

Contribution

It demonstrates that quenched disorder significantly slows quantum crystal melting without causing many-body localization, combining analytical and numerical evidence.

Findings

Disorder slows melting from ballistic to logarithmic.

No evidence of many-body localization in the system.

Complete melting occurs at extremely long timescales.

Abstract

The melting of the corner of a crystal is a classical, real-world, non-equilibrium statistical mechanics problem which has shown several connections with other branches of physics and mathematics. For a perfect, classical crystal in two and three dimensions the solution is known: the crystal melts reaching a certain asymptotic shape, which keeps expanding ballistically. In this paper, we move onto the quantum realm and show that the presence of quenched disorder slows down severely the melting process. Nevertheless, we show that there is no many-body localization transition, which could impede the crystal to be completely eroded. We prove such claim both by a perturbative argument, using the forward approximation, and via numerical simulations. At the same time we show how, despite the lack of localization, the erosion dynamics is slowed from ballistic to logarithmic, therefore pushing the complete melting of the crystal to extremely long timescales.