Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians

摘要

We study the dynamical density matrix renormalization group (DDMRG) andtime-dependent density matrix renormalization group (td-DMRG) algorithms in theab initio context, to compute dynamical correlation functions of correlatedsystems. We analyze the strengths and weaknesses of the two methods in smallmodel problems, and propose two simple improved formulations, DDMRG$^{++}$ andtd-DMRG$^{++}$, that give increased accuracy at the same bond dimension, at anominal increase in cost. We apply DDMRG$^{++}$ to obtain the oxygencore-excitation energy in the water molecule in a quadruple-zeta quality basis,which allows us to estimate the remaining correlation error in existing coupledcluster results. Further, we use DDMRG$^{++}$ to compute the local density ofstates and gaps, and td-DMRG$^{++}$ to compute the complex polarizationfunction, in linear hydrogen chains with up to 50 H atoms, to study metallicityand delocalization as a function of bond-length.