Abstract
Recently, the Density Matrix Renormalization Group (DMRG) has been extended to calculate the time evolution of an arbitrary state. Here, we will discuss this extension of the DMRG method, in particular, the general properties of the DMRG that are relevant to the extension, the basic issues that are involved in calculating timedependence within the DMRG, and the first attempts at formulating time-dependent DMRG (t-DMRG) algorithms. Moreoever, we describe adaptive t-DMRG methods, which tailor the reduced Hilbert space to one particular time step and which are therefore the most efficient algorithms for the majority of applications. Finally, we discuss in detail the application of the t-DMRG to a system of interacting spinless fermions which are quenched by suddenly changing the interaction strength. This system provides a very useful test bed for the method, but also raises physical issues which are illustrative of the general behavior of quenched interacting quantum systems.
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