Adaptive Lanczos-vector method for dynamic properties within the density matrix renormalization group

Dargel, Piet E.; Honecker, A.; Peters, Robert; Noack, R. M.; Pruschke, Thomas

doi:10.1103/physrevb.83.161104

Cited by 33 publications

(40 citation statements)

References 24 publications

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“…In fact, DMRG CFE refers to the method where all or some of the Lanczos vectors are targeted in the reduced density matrix at each DMRG step. In the original paper [3] by K. Hallberg all the Lanczos vectors are targeted, while in an improved version [20] by P.E. Dargel et al only three Lanczos vectors at a time are targeted as the lattice is swept.…”

Section: Conjugate Gradient and Krylov Methodsmentioning

confidence: 99%

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Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Nocera

Álvarez

2016

Phys. Rev. E

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Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand 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 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.

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Section: Conjugate Gradient and Krylov Methodsmentioning

confidence: 99%

“…Within the MPS formulation of DMRG, other powerful methods have been developed. [17,20,21] Ref. 20 and 21 have proposed an improvement of the continued fraction expansion method of Hallberg in the MPS language.…”

Section: Introductionmentioning

confidence: 99%

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Nocera

Álvarez

2016

Phys. Rev. E

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“…Nevertheless, the insets show that the manner in which the CheMPS peak heights increase with L is indeed consistent with Eq. (46)…”

Section: Finite-size Effectsmentioning

confidence: 99%

Chebyshev matrix product state approach for spectral functions

et al. 2011

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We show that recursively generated Chebyshev expansions offer numerically efficient representations for calculating zero-temperature spectral functions of one-dimensional lattice models using matrix product state (MPS) methods. The main features of this Chebychev matrix product state (CheMPS) approach are: (i) it achieves uniform resolution over the spectral function's entire spectral width; (ii) it can exploit the fact that the latter can be much smaller than the model's many-body bandwidth; (iii) it offers a well-controlled broadening scheme that allows finite-size effects to be either resolved or smeared out, as desired; (iv) it is based on using MPS tools to recursively calculate a succession of Chebychev vectors |tn , (v) whose entanglement entropies were found to remain bounded with increasing recursion order n for all cases analyzed here; (vi) it distributes the total entanglement entropy that accumulates with increasing n over the set of Chebyshev vectors |tn , which need not be combined into a single vector. In this way, the growth in entanglement entropy that usually limits density matrix renormalization group (DMRG) approaches is packaged into conveniently manageable units. We present zero-temperature CheMPS results for the structure factor of spin-antiferromagnetic Heisenberg chains and perform a detailed finite-size analysis. Making comparisons to three benchmark methods, we find that CheMPS (1) yields results comparable in quality to those of correction vector DMRG, at dramatically reduced numerical cost; (2) agrees well with Bethe Ansatz results for an infinite system, within the limitations expected for numerics on finite systems; (3) can also be applied in the time domain, where it has potential to serve as a viable alternative to time-dependent DMRG (in particular at finite temperatures). Finally, we present a detailed error analysis of CheMPS for the case of the noninteracting resonant level model.

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“…Note that existing methods for directly computing the Green's function, 26,[42][43][44][68][69][70] which are almost always formulated for finite systems, try to approximateÔ α | (A) , and sometimes…”

mentioning

confidence: 99%

Post-matrix product state methods: To tangent space and beyond

2013

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We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time evolution, excitations, and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well-defined quantum number. We present some illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post-matrix product methods.

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Adaptive Lanczos-vector method for dynamic properties within the density matrix renormalization group

Cited by 33 publications

References 24 publications

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Chebyshev matrix product state approach for spectral functions

Post-matrix product state methods: To tangent space and beyond

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