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Simulations by the hierarchical equations of motion with tensor trains

Étienne Mangaud, Amine Jaouadi, Joachim Galiana, Benjamin Lasorne, Alex W. Chin, Michèle Desouter-Lecomte

Published Dec 12, 2022• 0 citations
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We present a comprehensive theoretical study of charge transport in organic materials on the basis of the one-dimensional dispersive Holstein-Peierls model. The hierarchical equations of motion in tensor-train format (HEOM-TT) method is employed to accurately describe both local Holstein-type and nonlocal Peierls-type electron-phonon couplings in the presence of low-frequency dispersive phonons. Linear response formulation of carrier mobility is obtained by employing the generating functional method. We demonstrate the capability of the method by calculating current correlation functions, diffusivities, and mobilities for various transport regimes. Our results provide new insights into the mechanisms underlying charge transport in organic semiconductors and establish HEOM-TT as a powerful tool for studying complex vibronic quantum dynamics and transport properties in condensed matter systems.

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Hierarchical Equations of Motion (HEOM) in the Tensor-Train (TT) representation is applied to study the charge-transfer dynamics in organic semiconductors (OSCs). The theoretical formulation as well as the basic computational aspects of HEOM-TT are discussed in detail. Charge transfer in OSCs is modeled using dissipative polaronic models that incorporate the effects of both high- and low-frequency molecular vibrations, and it is simulated in a fully quantum and nonperturbative manner, which has not been studied intensively. The capability of treating complex electron-vibrational systems is examined by analyzing and comparing the numerical behavior of the time-dependent variational approach and the time-Alternating Minimal Energy methods and by calculating the current autocorrelation function and diffusivity across various models. Our results indicate that the HEOM-TT framework offers a robust tool for the detailed analysis of complex polaronic systems, suggesting its potential for broader applications.
We present a comprehensive theoretical study of charge transport in organic materials on the basis of the one-dimensional dispersive Holstein-Peierls model. The hierarchical equations of motion in tensor-train format (HEOM-TT) method is employed to accurately describe both local Holstein-type and nonlocal Peierls-type electron-phonon couplings in the presence of low-frequency dispersive phonons. Linear response formulation of carrier mobility is obtained by employing the generating functional method. We demonstrate the capability of the method by calculating current correlation functions, diffusivities, and mobilities for various transport regimes. Our results provide new insights into the mechanisms underlying charge transport in organic semiconductors and establish HEOM-TT as a powerful tool for studying complex vibronic quantum dynamics and transport properties in condensed matter systems.