Simulation of time evolution with multiscale entanglement renormalization ansatz

We describe an algorithm to simulate time evolution using the multiscale entanglement renormalization ansatz and test it by studying a critical Ising chain with periodic boundary conditions and with up to L approximate to 10(6) quantum spins. The cost of a simulation, which scales as L log(2)(L), is reduced to log(2)(L) when the system is invariant under translations. By simulating an evolution in imaginary time, we compute the ground state of the system. The errors in the g ound-state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.