Extending the range of real time density matrix renormalization group simulations

We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states |ψ〉 and operators A in the evaluation of 〈A〉ψ(t)=〈ψ|A(t)|ψ〉. This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics 〈A〉ρ(t)=Tr[ρA(t)] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T>0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T>0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.