Initial condition dependence of KPZ universality: from soft matter experiments to quantum spin chains

While the Kardar-Parisi-Zhang (KPZ) universality class has been established as a prominent class for random growth processes and many other stochastic problems in non-equilibrium but classical physics, it is only recently that KPZ turned out to rule quantum spin chains of the isotropic Heisenberg model. This implies that a wealth of knowledge from classical KPZ systems may be utilized to unveil characteristic statistical properties of the fluctuating quantum spins. Particularly noteworthy is the fact that the KPZ class splits into a few "universality subclasses" depending on the initial condition [1], which may potentially contribute to characterize thermalization of such quantum spins.

In the talk, I will first review main outcomes from the studies of the classical KPZ systems, mainly following experimental results on growing interfaces of liquid-crystal turbulence [1]. Emphasis will be put on the three representative universality subclasses and their characteristics, as well as the variational formula which can describe fluctuation properties from general initial conditions (see [2] and references therein, especially Quastel & Remenik 2014). Then I will describe how to "translate" these results to the problem of the quantum spin chains. In particular, I will focus on the non-Gaussian distribution of the polarization transfer found by quantum-gas microscopy by Bloch's group (Wei et al., arXiv:2107.00038) and describe our attempt to characterize it in terms of crossover between different universality subclasses.

The new results are from joint work with Y. T. Fukai, D. Wei, S. Gopalakrishnan, I. Bloch and J. Zeiher.