Thermalization of entanglement

Abstract

We explore the dynamics of the entanglement entropy near equilibrium in highly-entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with either less or more entanglement entropy than the equilibrium value, as well as the dynamics of the spontaneous fluctuations of the entanglement that occur in equilibrium. For the spin chain with a time-independent Hamiltonian and thus an extensive conserved energy, we find slow relaxation of the entanglement entropy near equilibration. Such slow relaxation is absent in a Floquet spin chain with a Hamiltonian that is periodic in time and thus has no local conservation law. Therefore, we argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system.

6 pages, 6 figures; as in journal

References in corpus (6)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization in Heisenberg XXZ magnet in a random field
• Equilibrium states of generic quantum systems subject to periodic driving
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Strong and weak thermalization of infinite non-integrable quantum systems
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Cited by in corpus (5)

• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Operator entanglement entropy of the time evolution operator in chaotic systems
• A Floquet Model for the Many-Body Localization Transition
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
• Entanglement dynamics and ergodicity breaking in a quantum cellular automaton