Hydrodynamics in long-range interacting systems with center-of-mass conservation

TL;DR

This paper develops a hydrodynamic theory for long-range interacting systems with center-of-mass conservation, revealing a rich phase diagram with various diffusive behaviors and supported by quantum lattice model simulations.

Contribution

It introduces a new hydrodynamic framework for long-range systems with center-of-mass conservation, highlighting the interplay of long-range interactions and conservation laws.

Findings

Identification of subdiffusive, diffusive, and superdiffusive phases

Continuous variation of dynamical exponents

Validation through quantum lattice model simulations

Abstract

In systems with a conserved density, the additional conservation of the center of mass (dipole moment) has been shown to slow down the associated hydrodynamics. At the same time, long-range interactions generally lead to faster transport and information propagation. Here, we explore the competition of these two effects and develop a hydrodynamic theory for long-range center-of-mass-conserving systems. We demonstrate that these systems can exhibit a rich dynamical phase diagram containing subdiffusive, diffusive, and superdiffusive behaviors, with continuously varying dynamical exponents. We corroborate our theory by studying quantum lattice models whose emergent hydrodynamics exhibit these phenomena.