  We provide numerical evidence that after a local quench in an isolated
infinite quantum spin chain, the quantum state locally relaxes to the ground
state of the post-quenched Hamiltonian, i.e. dissipates. This is a consequence
of the unitary quantum dynamics. A mechanism similar to the eigenstate
thermalization hypothesis is shown to be responsible for the dissipation
observed. We also demonstrate that integrability obstructs dissipation. The
numerical simulations are done directly in the thermodynamic limit with a
time-evolution algorithm based on matrix product states. The area law of
entanglement entropy is observed to hold after the local quench. As a result,
the simulations can be performed for long times with small bond dimensions.
Various local quenches on the Ising chain and the three-state Potts chain are
studied.
