Pushing the limits of the Density Matrix Renormalization Group: from vibrational spectroscopy to quantum dynamics
Simulation methods based on tensor factorizations, such as the density matrix renormalization group (DMRG) [1,2], are currently reshaping the limits of wave function-based quantum chemical algorithms. Tensor-based methods provide very compact parameterizations that can encode many-body wave functions by taming the high computational cost of Full Configuration Interaction and, therefore, enable large-scale exact quantum simulations. Chemical applications of DMRG have focused so far on time-independent electronic problems. In the present contribution, we show the potentiality of DMRG beyond this application field, by focusing on three simulation targets.
We first introduce the vibrational DMRG theory [3,4] to calculate the exact anharmonic vibrational energies of large molecular systems. Then, we apply DMRG to solve the time-dependent (TD) Schrödinger and show that the resulting algorithm, namely TD-DMRG [5,6], can accurately simulate ultrafast molecular processes occurring on multiple time-scales. Finally, we present an explicitly correlated DMRG variant, the transcorrelated DMRG (tc-DMRG) [7] that relies on the transcorrelated method [8] and enhances the accuracy of conventional DMRG for strongly-correlated molecules.
References:
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[2] A. Baiardi, M. Reiher, J. Chem. Phys., 2020, 152, 040903.
[3] A. Baiardi, C. J. Stein, V. Barone, M. Reiher, J. Chem. Theory Comput., 2017, 13, 3764–3777.
[4] A. Baiardi, C. J. Stein, V. Barone, M. Reiher, J. Chem. Phys., 2019, 150, 094113.
[5] A. Baiardi, M. Reiher, J. Chem. Theory Comput. 2019, 15, 3481–3498.
[6] A. Baiardi, ArXiv e-prints, 2020, 2010.02049.
[7] A. Baiardi, M. Reiher, J. Chem. Phys., 2020, 153, 164115.
[8] S. F. Boys, N. C. Handy, Proc. R. Soc. A Math. Phys. Eng. Sci., 1969, 310, 43–61.