KARDAR-PARISI-ZHANG PHYSICS IN A 2-DIMENSIONAL DISORDERED HONEYCOMB LATTICE

Patrik L. Ferrari, Tomohiro Sasamoto, Herbert Spohn

Pritha Dolai, Aditi Simha, Abhik Basu

We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We thus establish that the model belongs to the 1D KPZ universality class.

Kun Fang, Gayana Fernando, Alexander V. Balatsky +2 more

Alessandro Giuliani, Vieri Mastropietro

Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur

Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.

Pritha Dolai, Aditi Simha, Abhik Basu

We elucidate the universal spatiotemporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion processes. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal scaling exponents with the symmetries of the model equations. We thus establish that these models belong to the 1D KPZ universality class.