Simulation of time evolution with the MERA

Matteo Rizzi, Simone Montangero, Guifre' Vidal

Published 2007-06-06, updated 2008-04-24Version 2

We describe an algorithm to simulate time evolution using the Multi-scale Entanglement Renormalization Ansatz (MERA) and test it by studying a critical Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum spins. The cost of a simulation, which scales as L log(L), is reduced to log(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 ground state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.