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Abstract

Thermalization is investigated for the one-dimensional anisotropic
antiferromagnetic Heisenberg model with dimerized nearest-neighbor
interactions that break integrability. For this purpose the time
evolution of local operator expectation values after an interacting
quench is calculated directly with the Chebyshev polynomial expansion,
and the deviation of the diagonal from the canonical thermal ensemble
value is calculated for increasing system size for these operators. The
spatial and spin symmetries of the Hamiltonian are taken into account to
divide it into symmetry subsectors. The rate of thermalization is found
to weaken with the dimerization parameter as the Hamiltonian evolves
between two integrable limits, the non-dimerized and the fully dimerized
where the chain breaks up into isolated dimers. This conclusion is
supported by the distribution of the local operator off-diagonal
elements between the eigenstates of the Hamiltonian with respect to
their energy difference, which determines the strength of temporal
fluctuations. The off-diagonal elements have a low-energy peak for small
dimerization which facilitates thermalization, and originates in the
reduction of spatial symmetry with respect to the non-dimerized limit.
For increasing dimerization their distribution changes and develops a
single low-energy maximum that relates to the fully dimerized limit and
slows down thermalization.