A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model

TL;DR

This paper shows that specific initial states in the isotropic Heisenberg model can exhibit diffusive spin transport, contrasting the typical super-diffusive behavior, and provides a theoretical framework for understanding this phenomenon.

Contribution

It introduces a class of initial states that support diffusive spin dynamics in the isotropic Heisenberg model and derives a simple continuum equation describing their evolution.

Findings

Certain initial states lead to diffusive spin transport.

Bipartite entanglement entropy grows logarithmically in time.

Derived a continuum equation with solutions in terms of Fresnel integrals.

Abstract

The spin transport in isotropic Heisenberg model in the sector with zero magnetization is generically super-diffusive. Despite that, we here demonstrate that for a specific set of domain-wall-like initial product states it can instead be diffusive. We theoretically explain the time evolution of such states by showing that in the limiting regime of weak spatial modulation they are approximately product states for very long times, and demonstrate that even in the case of larger spatial modulation the bipartite entanglement entropy grows only logarithmically in time. In the limiting regime we derive a simple closed equation governing the dynamics, which in the continuum limit and for the initial step magnetization profile results in a solution expressed in terms of Fresnel integrals.