Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.

arXiv:1607.03538Physical review. ENov 21, 201691 citations

Dynamical Properties using the DMRG

Steven White

APSMar 1, 20010 citations

Spectral Functions with DMRG Revisited: Correction-vector with the Krylov-space Approach

Alberto Nocera, Gonzalo A. Álvarez

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand condensed matter experiments. Within the DMRG framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction-vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that Krylov-space approach can be more accurate and efficient than conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand condensed matter experiments. Within the DMRG framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction-vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that Krylov-space approach can be more accurate and efficient than conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.

Jul 12, 20161 citation

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

Alberto Nocera, G. Alvarez

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.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.

arXiv:2204.03165Physical review. B./Physical review. BNov 3, 202215 citations

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.