Topological Defects in Anisotropic Driven Open Systems

Abstract

We study the dynamics and unbinding transition of vortices in the compact anisotropic Kardar-Parisi-Zhang equation. The combination of nonequilibrium conditions and strong spatial anisotropy drastically affects the structure of vortices and amplifies their mutual binding forces, thus stabilizing the ordered phase. We find novel universal critical behavior in the vortex-unbinding crossover in finite-size systems. These results are relevant for a wide variety of physical systems, ranging from strongly coupled light-matter quantum systems to dissipative time crystals.

Vortex Dynamics in a Compact Kardar-Parisi-Zhang System

“…As has been shown by Sieberer and coworkers [5,8,9], by considering the dual electrodynamical (dED) picture of the cKPZ equation and a perturbative expansion in the nonlinear parameters λ, the vortices in the cKPZ system interact through a force with both conservative and nonconservative contributions due to the nonequilibrium nature of the system; in contrast to the equilibrium XY model, i.e., when λ x ¼ λ y ¼ 0, where the vortices interact through only central Coulomb forces [22,23]. However, in the present study we are interested in the scaling and critical properties of the system and, consequently, in the interdistance R between a vortex and an antivortex in a pair.…”

“…A paradigmatic example is the Berezinskii-Kosterlitz-Thouless (BKT) phase transition between disordered and ordered phases of the equilibrium planar XY model, caused by vortices binding at low temperatures due to their mutual attractive interactions [2,3]. Topological defects emerge naturally in a large number of nonequilibrium systems [4][5][6][7], although their roles at criticality are still largely unexplored. One paradigmatic case is the compact Kardar-Parisi-Zhang (cKPZ) equation [8,9], which appears as a natural extension of the noncompact KPZ equation, [10,11], when considering the compactness of the phase.…”

“…Recent theoretical studies suggest that the critical properties of 2D systems governed by the cKPZ equation differ substantially from their equilibrium counterparts, and that the BKT theory cannot be extended to all regimes [5,9,21]. This is rooted in the fact that the vortex-antivortex (V-AV) interactions in an isotropic or weakly anisotropic (WA) cKPZ system, in contrast to the equilibrium XY model, become repulsive beyond a characteristic length scale.…”

“…The cKPZ equation and the vortex interaction.-The cKPZ equation for compact variable θðr; tÞ reads [5,8]…”

“…Vortices in the system emerge as a consequence of the compactness of the θ variable in Eq. (1), since H ∇θdl ¼ 2πnðr; tÞ, with nðr; tÞ ∈ Z [5], where l is the contour. Consequently, nðr; tÞ ≠ 0 denotes a vortex with charge n, at site r and time t.…”