Abstract

Anomalous fluctuations are phenomena where hydrodynamic fluctuations in the system behave in a way that violates usual expectations, e.g. typical fluctuations that are Gaussian. It was discovered recently that certain many-body systems exhibit such fluctuations, and one of the most notable examples is the isotropic spin-1/2 Heisenberg chain whose spin transport shows a surprising “partial” Kardar-Parisi-Zhang (KPZ) physics. Such partial KPZ behaviour has been also experimentally confirmed using superconducting qubits, where it was observed that the higher spin cumulants behave in a way that is not controlled by any known KPZ sub universality class (e.g. GUE or Baik-Rains). In this talk, I will introduce a hydrodynamic framework based the ballistic macroscopic fluctuation theory to describe anomalous fluctuations and apply it to a class of stochastic cellular automata. The cellular automata, which have been solved microscopically, conserve a charge and it has been demonstrated that the charge fluctuations in these systems and the spin fluctuations in the easy-axis Heisenberg chain are both anomalous with the same non-Gaussian probability distribution function. I will show how our approach successfully reproduces the known typical and large charge fluctuations in the systems and explain how one can understand the phenomena hydrodynamically in systems with a Z_2 charge.