Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry

TL;DR

This paper develops an exact hydrodynamical framework for charge and operator dynamics in a U(1) symmetric quantum many-body system, revealing how charge transport influences operator behavior and quantum coherence.

Contribution

It introduces a novel SU(4) spin-chain mapping and a restricted Fokker-Planck equation to describe operator dynamics with charge conservation, highlighting the persistence of quantum coherence.

Findings

Quantum coherence persists after disorder averaging due to U(1) symmetry.

Charge transport significantly influences operator dynamics, even for operators without charge overlap.

The coupled operator-charge dynamics can be described by FKPP equations, applicable at all time scales.

Abstract

In this work, we derive an exact hydrodynamical description for the coupled, charge and operator dynamics, in a quantum many-body system with U(1) symmetry. Using an emergent symmetry in the complex Brownian SYK model with charge conservation, we map the operator dynamics in the model to the imaginary-time dynamics of an SU(4) spin-chain. We utilize the emergent SU(4) description to demonstrate that the U(1) symmetry causes quantum-coherence to persist even after disorder-averaging, in sharp contrast to models without symmetries. In line with this property, we write down a 'restricted' Fokker-Planck equation for the out-of-time ordered correlator (OTOC) in the large-$N$ limit, which permits a classical probability description strictly in the incoherent sector of the global operator-space. We then exploit this feature to describe the OTOC in terms of a Fisher-Kolmogorov-Petrovsky-Piskun (FKPP)-equation which couples the operator with the charge and is valid at all time-scales and for arbitrary charge-density profiles. The coupled equations obtained belong to a class of models also used to describe the population dynamics of bacteria embedded in a diffusive media. We simulate them to explore operator-dynamics in a background of non-uniform charge configuration, which reveals that the charge transport can strongly affect dynamics of operators, including those that have no overlap with the charge.