Anomalous transport in U(1)-symmetric quantum circuits

TL;DR

This paper studies transport phenomena in U(1)-symmetric disordered quantum circuits, revealing localized, diffusive, and superdiffusive behaviors, and introduces a new statistical measure to analyze these regimes.

Contribution

It develops a circular statistical moment to analyze transport and uncovers a unique prethermal superdiffusive regime in discrete-time systems.

Findings

Identification of localized, diffusive, and superdiffusive regimes

Introduction of a circular statistical moment for transport analysis

Discovery of a prethermal 'swappy' regime with coherent excitations

Abstract

In this work we investigate discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple function of the magnetization profile and which elegantly captures transport properties of the system. From this quantity we extract transport exponents, revealing behaviors across the phase diagram consistent with localized, diffusive, and - most interestingly for a disordered system - superdiffusive regimes. Investigation of this superdiffusive regime reveals the existence of a prethermal "swappy" regime unique to discrete-time systems in which excitations propagate coherently; even in the presence of strong disorder.