Projected Krylov Approach for Efficient Matrix Product State Based Computation of Real-frequency Spectral Functions*

We present a projected Krylov approach for efficient computation of real-frequency spectra on top of ground state (GS) matrix product states (MPS) obtained from the Density Matrix Renormalization Group (DMRG). Our method relies on projecting resolvents to the tangent space of the GS-MPS, where they can be efficiently represented using Krylov space techniques. This allows for a direct computation of spectral weights and their corresponding position on the real-frequency axis. We demonstrate the accuracy and efficiency of the projected Krylov method by showcasing spectral data for various models. These include the Haldane-Shastry model on a ring and free fermions on cylinders as benchmarks, as well as interacting fermionic models on cylinders as challenging and physically interesting applications.