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  • Letter
  • Open Access

Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

Jonas Richter* and Arijeet Pal

  • Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

  • *j.richter@ucl.ac.uk
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Phys. Rev. Research 4, L012003 – Published 14 January, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L012003

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 Letter 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 with 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.

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Phys. Rev. Research 4, L012003– Published 14 January, 2022
  • Received 13 August 2021
  • Accepted 9 December 2021
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