Emergent dipole moment conservation and subdiffusion in tilted chains

TL;DR

This paper investigates the transport behavior in an interacting tilted chain, revealing a crossover from diffusive to subdiffusive dynamics governed by the field strength and excitation wavelength, with emergent dipole conservation at high temperature.

Contribution

It demonstrates the emergent conservation of dipole moment in tilted chains and characterizes the diffusive to subdiffusive crossover based on field and wavelength.

Findings

Crossover scale between diffusion and subdiffusion is governed by F√L.

Subdiffusive dynamics persist at large fields but with exponentially suppressed transport.

Dipole moment is emergently conserved at infinite temperature.

Abstract

We study the transport dynamics of an interacting tilted (Stark) chain. We show that the crossover between diffusive and subdiffusive dynamics is governed by $F\sqrt{L}$, where $F$ is the strength of the field, and $L$ is the wave-length of the excitation. While the subdiffusive dynamics persist for large fields, the corresponding transport coefficient is exponentially suppressed with $F$ so that the finite-time dynamics appear almost frozen. We explain the crossover scale between the diffusive and subdiffusive transport by bounding the dynamics of the dipole moment for arbitrary initial state. We also prove its emergent conservation at infinite temperature. Consequently, the studied chain is one of the simplest experimentally realizable models for which numerical data are consistent with the hydrodynamics of fractons.