Thermalization Dynamics in Closed Quantum Many Body Systems: a Precision Large Scale Exact Diagonalization Study

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Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy.

• We systematically study the finite-size deviation between the resulting equilibrium state and the thermal state, and we highlight the importance of the energy variance on the deviations.
• We find that the deviations are well described by the eigenstate thermalization hypothesis, and that the von Neumann entropy correction scaling is the square of the local operator scaling.
• We reveal also an area law contribution to the relaxed von Neumann entropy, which we connect to the mutual information between the considered subsystem and its immediate environment.