Thermalization of a Dimerized Antiferromagnetic Spin Chain

TL;DR

This study examines how dimerization affects thermalization in a one-dimensional anisotropic antiferromagnetic Heisenberg model, revealing that increased dimerization slows thermalization due to changes in off-diagonal eigenstate elements.

Contribution

It provides a detailed analysis of the impact of dimerization on thermalization dynamics in a non-integrable quantum spin chain, highlighting the role of symmetry and eigenstate properties.

Findings

Thermalization rate decreases with increased dimerization.

Off-diagonal eigenstate elements influence the speed of thermalization.

Dimerization modifies the distribution of off-diagonal elements, affecting thermalization.

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.