Coupled Hydrodynamics in Dipole-Conserving Quantum Systems

TL;DR

This paper develops a hydrodynamic theory for charge and energy transport in dipole-conserving quantum systems, validated through numerical simulations and linked to ultracold atom experiments.

Contribution

It introduces a generic hydrodynamic framework for fractonic systems with dipole conservation and verifies it using a microscopic quantum field theory approach.

Findings

Derived a generalized diffusion matrix for dipole-conserving systems.

Validated hydrodynamic theory with numerical simulations.

Connected theoretical results to potential ultracold atom experiments.

Abstract

We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We formulate a generic hydrodynamic theory for this combination of fractonic constraints and numerically verify its applicability to the late-time dynamics of a specific bosonic quantum system by developing a microscopic non-equilibrium quantum field theory. Employing a self-consistent $1/N$ approximation in the number of field components, we extract all entries of a generalized diffusion matrix and determine their dependence on microscopic model parameters. We discuss the relation of our results to experiments in ultracold atom quantum simulators.