Enhancing (quasi-)long-range order in a two-dimensional driven crystal

TL;DR

This paper explores how non-equilibrium driving can enhance and sustain quasi-long-range order in two-dimensional driven crystals, even under thermal fluctuations, by suppressing large density fluctuations.

Contribution

It introduces a theoretical model combining thermal baths and momentum-conserving noise to explain long-range order violations and demonstrates its application through numerical simulations and potential experiments.

Findings

Non-equilibrium effects can suppress large density fluctuations.

The model predicts vanishing effective temperature for long-wavelength phonons.

Simulations show enhanced quasi-long-range order with parameter tuning.

Abstract

It has been recently shown that 2D systems can exhibit crystalline phases with long-range translational order showcasing a striking violation of the Hohenberg-Mermin-Wagner (HMW) theorem which is valid at equilibrium. This is made possible by athermal driving mechanisms that inject energy into the system without exciting long wavelength modes of the density field, thereby inducing hyperuniformity. However, as thermal fluctuations are superimposed on the non-equilibrium driving, long-range translational order is inevitably lost. Here, we discuss the possibility of exploiting non-equilibrium effects to suppress arbitrarily large density fluctuations even when a global thermal bath is coupled to the system. We introduce a model of a harmonic crystal driven both by a global thermal bath and by a momentum conserving noise, where the typical observables related to density fluctuations and long-range translational order can be analytically derived and put in relation. This model allows us to rationalize the violation of the HMW theorem observed in previous studies through the prediction of large-wavelength phonons which thermalize at a vanishing effective temperature when the global bath is switched off. The conceptual framework introduced through this theory is then applied to numerical simulations of a hard-disk solid in contact with a thermal bath and driven out-of-equilibrium by active collisions. Our numerical analysis demonstrates how varying driving and dissipative parameters can lead to an arbitrary enhancement of the quasi-long-range order in the system regardless of the applied global noise amplitude. Finally, we outline a possible experimental procedure to apply our results to a realistic granular system.