Measurement catastrophe and ballistic spread of charge density with vanishing current

TL;DR

This paper investigates a measurement catastrophe in many-body quantum systems with Hilbert-space fragmentation, revealing that charge density can spread ballistically even as current vanishes, indicating persistent memory effects.

Contribution

It provides a clear example demonstrating how charge density exhibits ballistic spread despite vanishing current, highlighting the phenomenon of measurement catastrophe in quantum jamming states.

Findings

Charge density spreads ballistically at late times.

Current approaches zero while charge density remains nontrivial.

Measurement effects have everlasting macroscopic impact.

Abstract

One of the features of many-body quantum systems with Hilbert-space fragmentation is the existence of stationary states manifesting quantum jamming. It was recently shown that these are "states with memory", in which, e.g., measuring a localised observable has everlasting macroscopic effects. We study such a measurement catastrophe with an example that stands out for its clarity. We show in particular that at late times the expectation value of a charge density becomes a nontrivial function of the ratio between distance and time notwithstanding the corresponding current approaching zero.