Dissipative dynamics in isolated quantum spin chains after a local quench*

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.