Explicit construction of quasi-conserved local operator of translationally invariant non-integrable quantum spin chain in prethermalization

Abstract

We numerically construct translationally invariant quasi-conserved operators with maximum range M which best-commute with a non-integrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasi-conserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasi-conserved operator can be understood as a dressed total "spin-z" operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasi-conserved operator.

arXiv comment22 pages with 13 pages of main text, 9 figures and 5 appendices (published version)

References in corpus (31)

• Chaos and Quantum Thermalization
• Efficient classical simulation of slightly entangled quantum computations
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Schrieffer-Wolff transformation for quantum many-body systems
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• Constructing local integrals of motion in the many-body localized phase
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Observation of Elastic Doublon Decay in the Fermi-Hubbard Model
• Disorder-Free Localization
• Prethermalization and universal dynamics in near-integrable quantum systems
• The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Prethermal Floquet Steady States and Instabilities in the Periodically Driven, Weakly Interacting Bose-Hubbard Model
• Quasi Many-body Localization in Translation Invariant Systems
• Dynamics of many-body localisation in a translation invariant quantum glass model
• Dynamics in many-body localized quantum systems without disorder
• Lifetime of double occupancies in the Fermi-Hubbard model
• Quantum Disentangled Liquids
• Thermalization and light cones in a model with weak integrability breaking
• Long coherence times for edge spins
• Asymptotic quantum many-body localization from thermal disorder
• Scenario for delocalization in translation invariant systems
• Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
• Explicit construction of local conserved operators in disordered many-body systems
• Slowest local operators in quantum spin chains
• Partial breakdown of quantum thermalization in a Hubbard-like model
• Quantum-disentangled liquid in the half-filled Hubbard model

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