Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain

Abstract

Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent $z=1$, none of the known variants of conformal invariance can act as its dynamical symmetry. In $d=1$ spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras, with the maximal finite-dimensional sub-algebra $\mathfrak{sl}(2,\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$. The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.

arXiv commentLatex 2e, 28 pp, 4 figures (revised, with 2 new figures)

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Cited by in corpus (5)

• Schrödinger symmetry: a historical review
• Dynamical universality classes of simple growth and lattice gas models
• Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
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