Connection between quantum-many-body scars and the AKLT model from the viewpoint of embedded Hamiltonians

Abstract

We elucidate the deep connection between the PXP model, which is a standard model of quantum many-body scars, and the AKLT Hamiltonian. Using the framework of embedded Hamiltonians, we establish the connection between the PXP Hamiltonian and the AKLT Hamiltonian, which clarifies the reason why the PXP Hamiltonian has nonthermal energy eigenstates similar to the AKLT state. Through this analysis, we find that the presence of such nonthermal energy eigenstates reflects the symmetry in the AKLT Hamiltonian.

11 pages, no figure

References in corpus (14)

• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Experimental Observation of a Generalized Gibbs Ensemble
• Localization from Hilbert space shattering: from theory to physical realizations
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
• Signatures of rare states and thermalization in a theory with confinement
• Systematic construction of scarred many-body dynamics in 1D lattice models
• Dynamical scar states in driven fracton systems
• Topological many-body scar states in dimensions 1, 2, and 3
• Thermalization without eigenstate thermalization hypothesis after a quantum quench

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• Quantum scars as embeddings of weakly "broken" Lie algebra representations
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• Slow quantum thermalization and many-body revivals from mixed phase space
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• Correspondence principle for many-body scars in ultracold Rydberg atoms
• Exact Floquet quantum many-body scars under Rydberg blockade
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• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
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• Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models
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• Topological Quantum Many-Body Scars in Quantum Dimer Models on the Kagome Lattice
• Quantum Many-Body Scars from Einstein-Podolsky-Rosen States in Bilayer Systems
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• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
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• Prethermal fragmentation in a periodically driven Fermionic chain
• Periodically driven Rydberg chains with staggered detuning
• Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space
• Quantum many-body scars in spin models with multibody interactions
• Strong Hilbert space fragmentation via emergent quantum drums in two dimensions
• Signatures of multifractality in a periodically driven interacting Aubry-André model
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• Dynamical route to ergodicity and quantum scarring in kicked coupled top
• Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
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• Classical route to ergodicity and scarring phenomena in a two-component Bose-Josephson junction
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Disorder enhanced quantum many-body scars in Hilbert crystals
• Quasi-Nambu-Goldstone modes in many-body scar models
• Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system
• Classical route to ergodicity and scarring in collective quantum systems
• Extreme many-body scarring in a quantum spin chain via weak dynamical constraints
• Stabilizer Scars
• Signatures of fragmentation for periodically driven fermions
• Nonmesonic Quantum Many-Body Scars in a 1D Lattice Gauge Theory
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• Stable dynamic helix state in the nonintegrable XXZ Heisenberg model
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• Constraint-induced breaking and restoration of ergodicity in spin-1 PXP models
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• Quantum transitions, ergodicity, and quantum scars in the coupled top model