Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

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.

8 pages, 5 figures (+ 5 pages, 6 figures)

References in corpus (24)

• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Glassy dynamics of kinetically constrained models
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Eigenstate thermalization within isolated spin-chain systems
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Diffusion in deterministic interacting lattice systems
• Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains
• Subdiffusion and many-body quantum chaos with kinetic constraints
• Gapless quantum spin chains: multiple dynamics and conformal wavefunctions
• Universal subdiffusion in strongly tilted many-body systems
• Quantum spin chains with multiple dynamics
• Hilbert space shattering and disorder-free localization in polar lattice gases
• Quantum scars and bulk coherence in a symmetry-protected topological phase
• Domain wall melting in spin-1 chains

Cited by in corpus (41)

• Random Quantum Circuits
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Hilbert Space Fragmentation and Commutant Algebras
• Subdiffusion and many-body quantum chaos with kinetic constraints
• Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models
• Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
• Superdiffusive Energy Transport in Kinetically Constrained Models
• Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Emergent tracer dynamics in constrained quantum systems
• Fracton superfluid hydrodynamics
• Hydrodynamics in long-range interacting systems with center-of-mass conservation
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Hilbert space fragmentation in a long-range system
• Quantum scars in spin-1/2 isotropic Heisenberg clusters
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Emergent strong zero mode through local Floquet engineering
• Corrections to diffusion in interacting quantum systems
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• The frustration-free fully packed loop model
• Local Hilbert space fragmentation and weak thermalization in Bose-Hubbard diamond necklaces
• Coherent spin-phonon scattering in facilitated Rydberg lattices
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
• Open-system spin transport and operator weight dissipation in spin chains
• Extreme many-body scarring in a quantum spin chain via weak dynamical constraints
• Non-thermal eigenstates and slow relaxation in quantum Fredkin spin chains
• Real-time broadening of bath-induced density profiles from closed-system correlation functions
• Can a spin chain relate combinatorics to number theory?
• Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions
• Space-time generalization of mutual information
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Subdiffusive transport in the Fredkin dynamical universality class
• Stable dynamic helix state in the nonintegrable XXZ Heisenberg model
• Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions
• Exact solution of the minimalist Stark many body localization problem in terms of spin pair hopping
• Anomalous relaxation of density waves in a ring-exchange system
• Hilbert space fragmentation from lattice geometry
• Symmetric tensor scars with tunable entanglement from volume to area law
• Superdiffusive transport in chaotic quantum systems with nodal interactions
• Diagnostics of Hilbert space fragmentation, freezing transition, and its effects in the family of quantum East models involving varying range of constraints
• Momentum-space modulated symmetries in the Luttinger liquid