Root- N Krylov-space correction vectors for spectral functions with the density matrix renormalization group

We propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-$N$ ($N=2$ is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure $N$ times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large $N$. We apply our method to spin and charge spectral functions of $t\text{\ensuremath{-}}J$ and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-$N$ approach reaches a much improved spectral resolution compared to the conventional correction vector.