Exact Anomalous Current Fluctuations in Quantum Many-Body Dynamics

TL;DR

This paper derives the first exact quantum many-body result showing that anomalous current fluctuations follow the M-Wright function, revealing universal transport behavior in a 1D Fermi-Hubbard model with strong interactions.

Contribution

It provides the first exact microscopic derivation of the M-Wright function for anomalous current fluctuations in quantum many-body systems.

Findings

Exact derivation of the M-Wright function in a quantum model

Analysis of integrated spin current in a 1D Fermi-Hubbard model

Establishment of universal anomalous transport behavior in quantum systems

Abstract

Fluctuations of integrated currents have attracted considerable interest over the past decades in the context of statistical mechanics. Recently, anomalous current fluctuations, characterized by the M-Wright function, were obtained exactly in a classical automaton [$\v{Z}$. Krajnik et al., Phys. Rev. Lett. 128, 160601 (2022)], and previous studies have shown that the anomalous behavior can arise in a variety of classical systems. Despite the rapidly growing interest in such anomalous behaviors, which capture a universal aspect of one-dimensional many-body transport, the exact derivation of the M-Wright function in quantum many-body systems has remained elusive. In this Letter, we present the first exact microscopic derivation of the M-Wright function in quantum many-body dynamics by analyzing the integrated spin current in a one-dimensional Fermi-Hubbard model with infinitely strong repulsive interactions. Our results lay the groundwork for exploring anomalous integrated currents in a broad class of quantum many-body systems.