Stochastic Adaptive Single-Site Time-Dependent Variational Principle

Xu, Yihe; Xie, Zhaoxuan; Xie, Xiaoyu; Schollwöck, Ulrich; Ma, Hao

doi:10.1021/jacsau.1c00474

Cited by 18 publications

(18 citation statements)

References 40 publications

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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%

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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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Section: Methodology and Algorithmmentioning

confidence: 99%

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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“…[76], which also has a parallel implementation [105], and the time-dependent variational principle (TDVP) algorithm, see, e.g., Refs. [86,87,[106][107][108][109]. In this work, we use the single-site TDVP, the two-site TDVP, and the parallel two-site TDVP (p2TDVP) algorithms introduced in Ref.…”

Section: Methodsmentioning

confidence: 99%

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

Jansen,

Bonča,

Heidrich-Meisner

2022

Preprint

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A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finitetemperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperatures. For the polaron in the weak and intermediate electron-phonon coupling regimes, we analyze the influence of phonon dispersion relations on the spectra. For strong electron-phonon coupling, the known result of an asymmetric Gaussian is reproduced for a flat phonon band. For a finite phonon bandwidth, the center of the Gaussian is either shifted to larger or smaller frequencies, depending on the sign of the phonon hopping. We illustrate that this can be well understood by considering the Born-Oppenheimer surfaces. A similar behavior is seen for the bipolaron for strong coupling. For the bipolaron with weak and intermediate coupling strengths and a flat phonon band, we obtain two very different spectra. The latter also has a temperature-dependent resonance at a frequency below the phonon frequency.

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“…Because different spin states share the same spectral density function we have N dir = 1. We perform the 2TDVP for the first half of the time followed by the stochastic adaptive one-site TDVP (SA-1TDVP) 53 to accelerate the computation. Other parameters are the same as in ref 40.…”

Section: Journal Of Chemicalmentioning

confidence: 99%

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Liu

Ma³

2023

J. Chem. Theory Comput.

Self Cite

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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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Stochastic Adaptive Single-Site Time-Dependent Variational Principle

Cited by 18 publications

References 40 publications

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

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

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

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