On the fly swapping algorithm for ordering of degrees of freedom in density matrix renormalization group.

Density matrix renormalization group (DMRG) and its time-dependent variants have found widespread applications in quantum chemistry, including ab initio electronic structure of complex bio-molecules, spectroscopy for molecular aggregates, and charge transport in bulk organic semiconductors. The underlying wavefunction ansatz for DMRG, matrix product state (MPS), requires mapping degrees of freedom (DOF) into a one-dimensional topology. DOF ordering becomes a crucial factor for DMRG accuracy. In this work, we propose swapping neighboring DOFs during the DMRG sweeps for DOF ordering, which we term 'on the fly swapping' (OFS) algorithm. We show that OFS is universal for both static and time-dependent DMRG with minimum computational overhead. Examples are given for one dimensional antiferromagnetic Heisenberg model, ab initio electronic structure of N ₂ molecule, and the S ₁ /S ₂ internal conversion dynamics of pyrazine molecule. It is found that OFS can indeed improve accuracy by finding better DOF ordering in all cases.
(© 2022 IOP Publishing Ltd.)