Fragmentation and emergent integrable transport in the weakly tilted Ising chain

TL;DR

This paper studies the weakly tilted Ising chain, revealing Hilbert space fragmentation, emergent integrability in certain sectors, and long-time ballistic transport, using exact integrable methods like Generalized Hydrodynamics.

Contribution

It uncovers emergent integrability and ballistic transport in the weakly tilted Ising chain, and analyzes the effects of integrability-breaking magnon clusters.

Findings

Hilbert space fragments into many sectors under weak tilt.

Isolated magnon sector exhibits integrable dynamics.

Ballistic transport persists over long times in this sector.

Abstract

We investigate emergent quantum dynamics of the tilted Ising chain in the regime of a weak transverse field. Within the leading order perturbation theory, the Hilbert space is fragmented into exponentially many decoupled sectors. We find that the sector made of isolated magnons is integrable with dynamics being governed by a constrained version of the XXZ spin Hamiltonian. As a consequence, when initiated in this sector, the Ising chain exhibits ballistic transport on unexpectedly long times scales. We quantitatively describe its rich phenomenology employing exact integrable techniques such as Generalized Hydrodynamics. Finally, we initiate studies of integrability-breaking magnon clusters whose leading-order transport is activated by scattering with surrounding isolated magnons.