Subdiffusive transport in the Fredkin dynamical universality class

TL;DR

This paper demonstrates that systems with Fredkin and Motzkin kinetic constraints exhibit subdiffusive transport, characterized by a specific conserved charge and an exact upper bound on the spectral gap, indicating slow dynamics.

Contribution

It identifies a pseudolocal conserved charge in Fredkin and Motzkin chains and derives an exact upper bound on their spectral gap, revealing subdiffusive transport behavior.

Findings

Subdiffusive transport with dynamical exponent z ≥ 5/2.

Existence of a pseudolocal conserved charge in these chains.

An exact upper bound on the spectral gap of order L^{-5/2}.

Abstract

We identify a pseudolocal conserved charge in the Fredkin and Motzkin quantum spin chains and explore its consequences for the hydrodynamics of systems with Fredkin- or Motzkin-type kinetic constraints. We use this quantity to formulate an exact upper bound ${\cal O}(L^{-5/2})$ on the gap of the Fredkin and Motzkin spin chains. Our results establish that transport in kinetically constrained dynamical systems with Fredkin or Motzkin constraints is subdiffusive, with dynamical exponent $z \geq 5/2$.