Generalized Gibbs Ensemble for Heisenberg Spin Chains

Abstract

We consider the Generalized Gibbs Ensemble (GGE) in the context of global quantum quenches in XXZ Heisenberg spin chains. Embedding the GGE into the Quantum Transfer Matrix formalism we develop an iterative procedure to fix the Lagrange-multipliers and to calculate predictions for the long-time limit of short-range correlators. The main idea is to consider truncated GGE's with only a finite number of charges and to investigate the convergence of the numerical results as the truncation level is increased. As an example we consider a quantum quench situation where the system is initially prepared in the Néel state and then evolves with an XXZ Hamiltonian with anisotropy Delta>1. We provide predictions for short range correlators and gather numerical evidence that the iterative procedure indeed converges. The results show that the system retains memory of the initial condition, and there are clear differences between the numerical values of the correlators as calculated from the purely thermal and the Generalized Gibbs ensembles.

21 pages, 12 figures. v2: minor changes, v3: minor changes

References in corpus (16)

• Thermalization and its mechanism for generic isolated quantum systems
• Time evolution of local observables after quenching to an integrable model
• Dephasing and the steady state in quantum many-particle systems
• Generalized Thermalization in an Integrable Lattice System
• Reduced Density Matrix after a Quantum Quench
• Quantum quench dynamics of the Luttinger model
• Effective thermal dynamics following a quantum quench in a spin chain
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Dynamical Correlations after a Quantum Quench
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Generalized TBA and generalized Gibbs
• Algebraic representation of correlation functions in integrable spin chains
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Global large time dynamics and the generalized Gibbs ensemble
• Quantum phase transitions and thermodynamics of quantum antiferromagnets with competing interactions

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• "Light-cone" dynamics after quantum quenches in spin chains
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• Prethermalization and universal dynamics in near-integrable quantum systems
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• Statistical localization: from strong fragmentation to strong edge modes
• Analytic results for a quantum quench from free to hard-core one dimensional bosons
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• Thermodynamics of quantum systems with multiple conserved quantities
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
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• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Quantum quenches from excited states in the Ising chain
• Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems
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• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
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• Pumping approximately integrable systems
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
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• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Integrability-protected adiabatic reversibility in quantum spin chains
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
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• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
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• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Non-equilibrium quantum relaxation across a localization-delocalization transition
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• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Iterative construction of conserved quantities in dissipative nearly integrable systems
• Strong Eigenstate Thermalization within a Generalized Shell in Noninteracting Integrable Systems
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• Critical quench dynamics of random quantum spin chains: Ultra-slow relaxation from initial order and delayed ordering from initial disorder
• Entanglement Pre-thermalization in an Interaction Quench between Two Harmonic Oscillators
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