Time‐dependent density matrix renormalization group method for quantum dynamics in complex systems

Abstract

The simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light-harvesting and spin transport, and so forth. In recent years, time-dependent density matrix renormalization group (TD-DMRG) has emerged as a general, numerically accurate and efficient method for highdimensional full-quantum dynamics. This review will cover the fundamental algorithms of TD-DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD-DMRG by benchmarking with the current state-of-the-art methods for simulating quantum dynamics of the spin-boson model and the Frenkel-Holstein(-Peierls) model. As applications of TD-DMRG to real-world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface.

Computational Method for Evaluating the Thermoelectric Power Factor for Organic Materials Modeled by the Holstein Model: A Time-Dependent Density Matrix Renormalization Group Formalism

“…The density matrix renormalization group (DMRG) is a numerically accurate and robust method for many-body problems. 46 Since the establishment by White in 1992, 47 numerous algorithms have been developed, including timeevolution algorithms, 48,49 finite-temperature algorithms, 50 etc. The rapid development of algorithms enables DMRG to tackle various problems, including strong correlation lattice models, 51 ab initio electronic structure, 52,53 and excited-state dynamics.…”

Computational Method for Evaluating the Thermoelectric Power Factor for Organic Materials Modeled by Holstein Model: A Time-Dependent Density Matrix Renormalization Group Formalism

“…Density matrix renormalization group (DMRG) is a numerically accurate and robust method for many-body problems 46 . Since the establishment by White in 1992 47 , numerous algorithms have been developed, including time-evolution algorithms 48,49 , finite temperature algorithms 50 , etc.…”

Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems

“…Spectral functions such as local density of states (LDOS) and photoemission spectrum bridge the gap between theory and experiment. Calculating the spectral functions of models with both strong electron-electron and electron-phonon interactions is challenging [37][38][39]. For example, several methods have been used to study the spectral functions of HHM but suffer from their inherent limitations.…”