Analytic response theory for the density matrix renormalization group

Abstract

We propose an analytic response theory for the density matrix renormalisation group whereby response properties correspond to analytic derivatives of density matrix renormalisation group observables with respect to the applied perturbations.Both static and frequency-dependent response theories are formulated and implemented. We evaluate our pilot implementation by calculating static and frequencydependent polarisabilities of short oligo-di-acetylenes. The analytic response theory is competitive with dynamical density matrix renormalisation group methods and yields significantly improved accuracies when using a small number of density matrix renormalisation group states. Strengths and weaknesses of the analytic approach are discussed.

Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states

“…In addition, further conditions must also be placed on the first order changes in the left-and right-rotation matrices. In previous work, 21 it was shown that these conditions are…”

“…This was first proposed by Dorando et al 21 in the DMRG context, and later recast in the MPS language by Haegeman et al, 24,25 by means of the time-dependent variational principle (TDVP). 23 Here, we follow Dorando's work in order to use the DMRG context in what follows.…”

“…In Ref. 21, this was achieved by writing down the linear response equations for the left and right rotation matrices in terms of the first order density matrices. For the left rotation matrix, the response equation is of the form…”

“…One way to relieve this drawback of the SA-DMRG algorithm is to use the stateaveraged harmonic Davidson (SA-HD) DMRG algorithm to target higher excited states directly. 20 Recently, excitations have been constructed on top of a reference MPS wavefunction, [21][22][23][24][25][26][27] analogous to the concept of particle-hole excitations on top of a reference Slater determinant. In this post-MPS or post-DMRG theory, the reference MPS wavefunction provides a site-based meanfield ansatz, 22,28 and excitations consist of "local" changes in this mean-field ansatz.…”

The ab-initio density matrix renormalization group in practice

“…Since then, many groups have independently implemented and improved on the ab-initio DMRG algorithm. Some of these improvements include parallelization, 8,20 nonAbelian symmetry and spin-adaptation, 7,[21][22][23] orbital ordering 5,[24][25][26] and optimization, 9,27-29 more sophisticated initial guesses, 5,24,25,30,31 better noise algorithms, 5,32 extrapolation procedures, 5,33,34 response theories, 35,36 as well as the combination of the DMRG with various other quantum chemistry methods such as perturbation theory, 37 canonical transformations, 38 configuration interaction, 39 and relativistic Hamiltonians. 40 In the ecosystem of quantum chemistry, the DMRG occupies a unique spot.…”