Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics

TL;DR

This paper investigates the conformal invariance of loop ensembles in a lozenge tiling model under KPZ dynamics, revealing invariance in one component and breaking in another, with implications for critical phenomena.

Contribution

It demonstrates numerically that conformal invariance persists in the stationary KPZ state for certain loop ensembles, extending understanding of non-equilibrium surface models.

Findings

Conformal invariance appears in the stationary KPZ state.

Signatures of critical percolation are observed.

Invariance of one Coulomb gas component under KPZ dynamics.

Abstract

We study scaling properties of the honeycomb fully packed loop ensemble associated with a lozenge tiling model of rough surface, when the latter is driven out of equilibrium by Kardar-Parisi-Zhang (KPZ) type dynamics. We show numerically that conformal invariance and signatures of critical percolation appear in the stationary KPZ state. In terms of the two-component Coulomb gas description of the Edwards-Wilkinson stationary state, our finding is understood as the invariance of one component under the effect of the non-linear KPZ term. On the other hand, we show a breaking of conformal invariance when the level lines of the other component are considered.