From higher-order moments to time correlation functions in strongly correlated systems: A DMRG-based memory kernel coupling theory

Abstract: We introduce a hybrid approach for computing dynamical observables in strongly correlated systems using higher-order moments. This method integrates memory kernel coupling theory (MKCT) with the density matrix renormalization group (DMRG), extending our recent work on MKCT to strongly correlated systems. The method establishes that correlation functions can be derived from the moments. Within our framework, operators and wavefunctions are represented as matrix product operators (MPOs) and matrix product states (MPSs), respectively. Crucially, the repeated application of the Liouville operator is achieved through an iterative procedure analogous to the DMRG algorithm itself. We demonstrate the effectiveness and efficiency of MKCT-DMRG by computing the spectral function of the Hubbard model. Furthermore, we successfully apply the method to compute the electronic friction in the Hubbard-Holstein model. In all cases, the results show excellent agreement with time-dependent DMRG (TD-DMRG) benchmarks. The advantage of MKCT-DMRG over TD-DMRG is the computational efficiency, which avoids expensive real-time propagation in TD-DMRG. These findings establish MKCT-DMRG as a promising and accurate framework for simulating challenging dynamical properties in strongly correlated quantum systems.