Computing Spectral functions of strongly correlated Hamiltonians using DMRG: root-N Krylov space approach for correction-vectors

We propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) method directly in frequency space, based on a modified Krylov space approach to compute the correction-vectors. The 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. Even though the approach still involves separate calculations for different target frequencies, we show that it greatly alleviates the burden of keeping a large bond dimension as in the standard correction-vector DMRG method, while achieving better computational performance at large N. Finally, we apply this approach to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry, showing that it also reaches a much improved resolution at large frequencies.