Eigenstate Thermalization and its breakdown in Quantum Spin Chains with Inhomogeneous Interactions

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.