  The eigenstate thermalization hypothesis (ETH) is a successful theory that
establishes the criteria for ergodicity and thermalization in isolated quantum
many-body systems. In this work, we investigate the thermalization properties
of spin-$ 1/2 $ XXZ chain with linearly-inhomogeneous interactions. We
demonstrate that introduction of the inhomogeneous interactions leads to an
onset of quantum chaos and thermalization, which, however, becomes inhibited
for sufficiently strong inhomogeneity. To exhibit ETH, and to display its
breakdown upon varying the strength of interactions, we probe statistics of
energy levels and properties of matrix elements of local observables in
eigenstates of the inhomogeneous XXZ spin chain. Moreover, we investigate the
dynamics of the entanglement entropy and the survival probability which further
evidence the thermalization and its breakdown in the considered model. We
outline a way to experimentally realize the XXZ chain with
linearly-inhomogeneous interactions in systems of ultracold atoms. Our results
highlight a mechanism of emergence of ETH due to insertion of inhomogeneities
in an otherwise integrable system and illustrate the arrest of quantum dynamics
in presence of strong interactions.
