Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

TL;DR

This paper explores how quantum scars and weak Hilbert space fragmentation in a one-dimensional spin-1 frustration-free Hamiltonian lead to anomalous hydrodynamics, including subdiffusive spin transport and localized dynamics.

Contribution

It introduces a new class of deformed Motzkin chains exhibiting unique interplay between scarring and fragmentation, revealing distinct dynamical universality classes.

Findings

Quantum scars embedded in disjoint Krylov subspaces cause slow entanglement growth.

Spin transport at infinite temperature is subdiffusive, confirmed by cellular automaton simulations.

Deformed Motzkin chains form a different universality class from dipole-conserving systems.

Abstract

Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with dipole and $U(1)$ conservation, the fragmentation results in subdiffusive transport. In this paper we study the interplay between scarring and weak fragmentation giving rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$ frustration-free projector Hamiltonians, known as deformed Motzkin chain. The ground states and low-lying excitations of these chains exhibit large entanglement and critical slowdown. We show that at high energies the particular form of the projectors causes the emergence of disjoint Krylov subspaces for open boundary conditions, with an exact quantum scar being embedded in each subspace, leading to slow growth of entanglement and localized dynamics for specific out-of-equilibrium initial states. Furthermore, focusing on infinite temperature, we unveil that spin transport is subdiffusive, which we corroborate by simulations of constrained stochastic cellular automaton circuits. Compared to dipole moment conserving systems, the deformed Motzkin chain appears to belong to a different universality class with distinct dynamical transport exponent and only polynomially many Krylov subspaces.