Quantum dynamics (QD) simulation is a powerful tool for interpreting ultrafast spectroscopy experiments and unraveling their microscopic mechanism in out-of-equilibrium excited state behaviors in various chemical, biological, and material systems. Although state-of-the-art numerical QD approaches such as the time-dependent density matrix renormalization group (TD-DMRG) already greatly extended the solvable system size of general linearly coupled exciton-phonon models with up to a few hundred phonon modes, the accurate simulation of larger system sizes or strong system-environment interactions is still computationally highly challenging. Based on quantum information theory (QIT), in this work, we realize that only a small number of effective phonon modes couple to the excitonic system directly regardless of a large or even infinite number of modes in the condensed phase environment. On top of the identified small number of direct effective modes, we propose a hierarchical mapping (HM) approach through performing block Lanczos transformations on the remaining indirect modes, which transforms the Hamiltonian matrix to a nearly block-tridiagonal form and eliminates the long-range interactions. Numerical tests on model spin-boson systems and realistic singlet fission models in a rubrene crystal environment with up to 7000 modes and strong system-environment interactions indicate HM can reduce the system size by 1-2 orders of magnitude and accelerate the calculation by ∼80% without losing accuracy.
Quantum dynamics (QD) simulation is a powerful tool for interpreting ultrafast spectroscopy experiments and unraveling their microscopic mechanism in out-of-equilibrium excited state behaviors in various chemical, biological, and material systems. Although state-of-the-art numerical QD approaches such as the time-dependent density matrix renormalization group (TD-DMRG) already greatly extended the solvable system size of general linearly coupled exciton-phonon models with up to a few hundred phonon modes, the accurate simulation of larger system sizes or strong system-environment interactions is still computationally highly challenging. Based on quantum information theory (QIT), in this work, we realize that only a small number of effective phonon modes couple to the excitonic system directly regardless of a large or even infinite number of modes in the condensed phase environment. On top of the identified small number of direct effective modes, we propose a hierarchical mapping (HM) approach through performing block Lanczos transformations on the remaining indirect modes, which transforms the Hamiltonian matrix to a nearly block-tridiagonal form and eliminates the long-range interactions. Numerical tests on model spin-boson systems and realistic singlet fission models in a rubrene crystal environment with up to 7000 modes and strong system-environment interactions indicate HM can reduce the system size by 1-2 orders of magnitude and accelerate the calculation by ∼80% without losing accuracy.
It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system-bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system-bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system-bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system-bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system-bath couplings using matrix product states, which may further our understanding of nonlocal exciton-phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.
Dynamical electronic- and vibrational-structure theories have received a growing interest in the past few years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular system can, in principle, be obtained from the time-dependent version of full configuration interaction. Such an approach is, however, limited to few-atom systems due to the exponential increase of its cost with the system dimension. In the present work, we overcome this unfavorable scaling by employing the time-dependent density matrix renormalization group (TD-DMRG) which parametrizes the time-dependent wave function as a matrix product state. The time-dependent Schrödinger equation is then integrated with a sweep-based algorithm, as in standard time-independent DMRG. Unlike other TD-DMRG approaches, the one presented here leads to a set of coupled equations that can be integrated exactly. The resulting theory enables us to study real- and imaginary-time evolutions of Hamiltonians comprising more than 20 degrees of freedom that are challenging for current state-of-the-art quantum dynamics algorithms. We apply our algorithm to the simulation of quantum dynamics of models of increasing complexity, ranging from simple excitonic Hamiltonians to more complex ab initio vibronic ones.
Thanks to the high compression of the matrix product state (MPS) form of the wave function and the efficient site-by-site iterative sweeping optimization algorithm, the density matrix normalization group (DMRG) and its time-dependent variant (TD-DMRG) have been established as powerful computational tools in accurately simulating the electronic structure and quantum dynamics of strongly correlated molecules with a large number (10 1–2 ) of quantum degrees of freedom (active orbitals or vibrational modes). However, the quantitative characterization of the quantum many-body behaviors of realistic strongly correlated systems requires a further consideration of the interaction between the embedded active subsystem and the remaining correlated environment, e.g., a larger number (10 2–3 ) of external orbitals in electronic structure or infinite condensed-phase phononic modes in nucleus dynamics. To this end, we introduced three new post-DMRG and TD-DMRG approaches, namely (1) DMRG2sCI-MRCI and DMRG2sCI-ENPT by the reconstruction of selected configuration interaction (sCI) type of compact reference function from DMRG coefficients and the use of externally contracted MRCI (multireference configuration interaction) and Epstein–Nesbet perturbation theory (ENPT), without recourse to the expensive high order n -electron reduced density matrices ( n -RDMs). (2) DMRG combined with RR-MRCI (renormalized residue-based MRCI), which improves the computational accuracy and efficiency of internally contracted (ic) MRCI by renormalizing the contracted bases with small-sized buffer environment(s) of a few external orbitals as probes based on quantum information theory. (3) HM (hierarchical mapping)-TD-DMRG in which a large environment is reduced to a small number of renormalized environmental modes (which accounts for the most vital system–environment interactions) through stepwise mapping transformation. These advances extend the efficacy of highly accurate DMRG/TD-DMRG computations to the quantitative characterization of the electronic structure and quantum dynamics in realistic strongly correlated systems coupled with large environments and are reviewed in this paper.
The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.
Electronic and/or vibronic coherence has been found by recent ultrafast spectroscopy experiments in many chemical, biological, and material systems. This indicates that there are strong and complicated interactions between electronic states and vibration modes in realistic chemical systems. Therefore, simulations of quantum dynamics with a large number of electronic and vibrational degrees of freedom are highly desirable. Due to the efficient compression and localized representation of quantum states in the matrix-product state (MPS) formulation, time-evolution methods based on the MPS framework, which we summarily refer to as tDMRG (time-dependent density-matrix renormalization group) methods, are considered to be promising candidates to study the quantum dynamics of realistic chemical systems. In this work, we benchmark the performances of four different tDMRG methods, including global Taylor, global Krylov, and local one-site and two-site time-dependent variational principles (1TDVP and 2TDVP), with a comparison to multiconfiguration time-dependent Hartree and experimental results. Two typical chemical systems of internal conversion and singlet fission are investigated: one containing strong and high-order local and nonlocal electron-vibration couplings and the other exhibiting a continuous phonon bath. The comparison shows that the tDMRG methods (particularly, the 2TDVP method) can describe the full quantum dynamics in large chemical systems accurately and efficiently. Several key parameters in the tDMRG calculation including the truncation error threshold, time interval, and ordering of local sites were also investigated to strike the balance between efficiency and accuracy of results.
The strength of the density matrix renormalization group (DMRG) in handling strongly correlated systems lies in its unbiased and simultaneous treatment of identical sites that are both energetically degenerate and spatially similar, as typically encountered in physical models. However, this very feature becomes a drawback when DMRG is applied to quantum chemistry calculations for large, realistic correlated systems. This is because entangled orbitals often span broad ranges in both energy and space, with their interactions being notably inhomogeneous. In this study, we suggest addressing the strong intrafragment correlations and weak interfragment correlations separately, utilizing a large-scale multiconfigurational calculation framework grounded in the block interaction product state formulation. The strong intrafragment correlation can be encapsulated in several electronic states located on fragments, which are obtained by considering the entanglement between fragments and their environments. Moreover, we incorporate non-Abelian spin-SU(2) symmetry in our work to target the desired states we interested with well-defined particle number and spin, providing deeper insights into the corresponding chemical processes. The described method has been examined in various chemical systems and demonstrates high efficiency in addressing the inhomogeneous effects in strong correlation quantum chemistry.