Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems

Abstract

The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modelling the time evolution as cellular automata for specific cases of dipole-and quadrupole-conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher moment conservation.

Hydrodynamics in lattice models with continuous non-Abelian symmetries

“…We first describe fluids with a conserved U(1) charge and dipole moment, whose hydrodynamics was recently formulated in [58]; see also [59][60][61][62]. An instructive cartoon is to start by supposing that there is a local conserved density ρ corresponding to charge, and s i corresponding to local dipole density orthogonal to x i ρ: namely, the total conserved dipole moment can be written as…”

Transport through interacting defects and lack of thermalisation

“…Secondly, here, we focused on the case where the bulk Hamiltonian is free and interacting-integrable bulk Hamiltonians are a natural next step to be addressed: the study of collision terms in the framework of Generalized Hydrodynamics is still at its infancy [70][71][72], but an analysis in the same spirit of our kinetic equation can be envisaged. Beside integrability, there are several ways to hinder thermalisation while retaining non-trivial transport, such as Hilbert space fragmentation [9,73] and it is natural to wonder about interfaces between fragmenting and non-fragmenting Hamiltonians.…”

Space-Dependent Symmetries and Fractons

“…Therefore, the system is diffusive but compared to ordinary diffusion where the spatial width of a distribution increases as a square root of time Δx ∼ t 1/2 , the conservation of higher multipole charges slows down the process to Δx ∼ t 1/(n+1) , i.e. it is subdiffusive [87][88][89][90][91][92][93][94].…”