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arXiv · 2204.03165

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

Alberto Nocera·Gonzalo Alvarez
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Abstract

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, while achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry, and provide evidence that the root-N approach reaches a much improved resolution compared to conventional correction-vector.

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Alberto Nocera, Gonzalo Alvarez. 2022-04-07. Root-N Krylov-space correction-vectors for spectral functions with the density matrix renormalization group. https://doi.org/10.1103/physrevb.106.205106

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