Information Scrambling in Free Fermion Systems with a Sole Interaction

TL;DR

This paper explores how a single interaction affects quantum information scrambling in free fermion systems, revealing diffusive and exponential growth regimes depending on system connectivity.

Contribution

It introduces models with a single interaction in free fermion circuits and maps operator growth to a symmetric exclusion process, highlighting new dynamics of scrambling.

Findings

Operator scrambling occurs in both circuit types.

Diffusive scaling of operator and entanglement in 1D systems.

Exponential operator growth and linear entanglement increase in all-to-all hopping.

Abstract

It is well established that the presence of single impurity can have a substantial impact on the transport properties of quantum many-body systems at low temperature. In this work, we investigate a close analog of this problem from the perspective of quantum information dynamics. We construct Brownian circuits and Clifford circuits consisting of a free fermion hopping term and a sole interaction. In both circuits, our findings reveal the emergence of operator scrambling. Notably, the growth of the operator can be mapped to the symmetric exclusion process in the presence of a source term localized at a single point. We demonstrate that in the one-dimensional system, both the operator and entanglement exhibit diffusive scaling. Conversely, in scenarios characterized by all-to-all hopping, the operator's size undergoes exponential growth, while the entanglement exhibits a linear increase over time.