Conservation Laws and Integrability of a One-dimensional Model of Diffusing Dimers

TL;DR

This paper analyzes a one-dimensional assisted diffusion model of hard-core particles, revealing its integrability, sector decomposition, and unique long-time correlation decay behaviors, with implications for hydrodynamics.

Contribution

It provides an exact sector decomposition and demonstrates the model's integrability and symmetries, linking it to the Heisenberg model and revealing new long-time decay behaviors.

Findings

Exact sector decomposition of the configuration space.

Model is equivalent to the Heisenberg model and integrable.

Different sectors exhibit qualitatively distinct long-time decay of correlations.

Abstract

We study a model of assisted diffusion of hard-core particles on a line. The model shows strongly ergodicity breaking : configuration space breaks up into an exponentially large number of disconnected sectors. We determine this sector-decomposion exactly. Within each sector the model is reducible to the simple exclusion process, and is thus equivalent to the Heisenberg model and is fully integrable. We discuss additional symmetries of the equivalent quantum Hamiltonian which relate observables in different sectors. In some sectors, the long-time decay of correlation functions is qualitatively different from that of the simple exclusion process. These decays in different sectors are deduced from an exact mapping to a model of the diffusion of hard-core random walkers with conserved spins, and are also verified numerically. We also discuss some implications of the existence of an infinity of conservation laws for a hydrodynamic description.