Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states

Dunnett, Angus; Chin, Alex W.

doi:10.1103/physrevb.104.214302

Cited by 26 publications

(17 citation statements)

References 57 publications

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“…The 1TDVP has a larger projection error than the 2TDVP, and the standard 1TDVP cannot increase the bond dimensions of the MPS during time evolution to meet the entanglement growth. To improve this, some studies embed the dynamical bond dimension into the 1TDVP. − For real calculations, it is important to combine the different implementations of the TDVP.…”

Section: Methodsmentioning

confidence: 99%

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Liu

Ma³

2023

J. Chem. Theory Comput.

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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.

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Section: Methodsmentioning

confidence: 99%

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Liu

Ma³

2023

J. Chem. Theory Comput.

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“…However, compared to the standard one‐site algorithm, the strict TDVP is violated and in addition, the computational scaling is larger. Recently, further development of the one‐site TDVP‐PS algorithm is also able to adaptively optimize the bond dimension, which avoids the high‐computational cost of the two‐site algorithm 123–125 …”

Section: Methodology and Algorithmmentioning

confidence: 99%

“…Recently, further development of the one-site TDVP-PS algorithm is also able to adaptively optimize the bond dimension, which avoids the high-computational cost of the two-site algorithm. [123][124][125] Because the TDVP-VMF/CMF scheme and the TDVP-PS scheme are both based on TDVP, jΨ(t)i should be the same if not considering the error of the integrator. With regard to the time step size, in contrast to P&C-RK, the error will have a monotonic relationship with it.…”

Section: Tdvp-psmentioning

confidence: 99%

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

Ren

Jiang

et al. 2022

WIREs Comput Mol Sci

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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.

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“…The ordering of the modes may be an important factor influencing the efficiency of Time Dependent Variational Principle (TDVP) methods [97]. Further improvements are currently underway to consider the reorganization of the modes [72,98], rank adaptative methods [37,56,[99][100][101] or hierarchical tensor train approach [55].…”

Section: Oct By Tensor Trainsmentioning

confidence: 99%

Laser-controlled electronic symmetry breaking in a phenylene ethynylene dimer: Simulation by the hierarchical equations of motion and optimal control

et al. 2022

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The ability to prepare a specific superposition of electronic excited states leading to a transitory symmetry breaking of the electronic density in complex systems remains a challenging concern. We investigate how an initial coherence can be controlled by laser fields. The selected molecular system is a symmetric dimer of phenylene ethynylene presenting different interesting properties: two bright nearly degenerate excited states coupled through a conical intersection are addressable by orthogonal transition dipole moments and are well separated from neighboring states. Creating a superposed state with equal weights corresponds to a right or left electronic localization as in the double-well system followed by a transitory oscillation between the two wells. To ensure a spectral bandwidth typically smaller than 0.25 eV, the pulse duration is in the tens of femtoseconds range so that nuclear motion cannot be neglected. Optimal control theory (OCT) is applied with guess fields that effectively create the target coherence in the absence of dephasing due to the vibrational baths. We analyze the field reshaping proposed by the control and we further fit sequence of pulses on the optimal field. The overall result is efficient and robust disymmetry control over reasonable time scales of few tens of femtoseconds, exceeding the pulse duration. The monotonically convergent algorithm is combined with the hierarchical equations of motion (HEOM) able to treat strongly coupled non-Markovian dynamics. We also check the implementation of the combined OCT-HEOM approach in the tensor-train (TT) representation with propagation using the time dependent variational method.

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Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states

Cited by 26 publications

References 57 publications

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

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

Laser-controlled electronic symmetry breaking in a phenylene ethynylene dimer: Simulation by the hierarchical equations of motion and optimal control

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