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arXiv:2410.12285 · The Journal of Chemical Physics

Hamiltonian non-Hermicity: Accurate dynamics with the multiple Davydov D2Ansätze

Lixing Zhang, Kaijun Shen, Yiying Yan, Kewei Sun, Maxim F. Gelin, Yang Zhao

Published Nov 19, 2024• 9 citations
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Abstract

We examine the applicability of the numerically accurate method of time dependent variation with multiple Davydov Ansätze (mDA) to non-Hermitian systems. As illustrative examples, three systems of interest have been studied, a non-Hermitian system of dissipative Landau-Zener transitions, a non-Hermitian multimode Jaynes-Cummings model, and a dissipative Holstein-Tavis-Cummings model, all of which are shown to be effectively described by the mDA method. Our findings highlight the versatility of the mDA as a powerful numerical tool for investigating complex many-body non-Hermitian systems, which can be extended to explore diverse phenomena such as skin effects, excited-state dynamics, and spectral topology in the non-Hermitian field.

DOI
10.1063/5.0243861

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We examine the applicability of the numerically accurate method of time dependent variation with multiple Davydov Ansätze (mDA) to non-Hermitian systems. As illustrative examples, three systems of interest have been studied, a non-Hermitian system of dissipative Landau-Zener transitions, a non-Hermitian multimode Jaynes-Cummings model, and a dissipative Holstein-Tavis-Cummings model, all of which are shown to be effectively described by the mDA method. Our findings highlight the versatility of the mDA as a powerful numerical tool for investigating complex many-body non-Hermitian systems, which can be extended to explore diverse phenomena such as skin effects, excited-state dynamics, and spectral topology in the non-Hermitian field.
We perform benchmark simulations using the time-dependent variational approach with the multiple Davydov Ansatz (mDA) to study real-time nonequilibrium dynamics in a single qubit model coupled to two thermal baths with distinct temperatures. A broad region of the parameter space has been investigated, accompanied by a detailed analysis of the convergence behavior of the mDA method. In addition, we have compared our mD2 results to those from two widely adopted, numerically "exact" techniques: the methods of hierarchical equations of motion (HEOM) and the quasi-adiabatic path integral (QUAPI). It is found that the mDA approach in combination with thermal field dynamics yields numerically accurate, convergent results in nearly all regions of the parameter space examined, including those that pose serious challenges for QUAPI and HEOM. Our results reveal that mDA offers a highly adaptable framework capable of capturing long-time dynamics, even in challenging regimes where other methods face limitations. These findings underscore the potential of mDA as a versatile tool for exploring quantum thermodynamics, energy transfer processes, and non-equilibrium quantum systems.
Davydov trial states, in combination with the Green's function method, we study the dynamics of the Tavis-Cummings model and the Holstein-Tavis-Cummings model in the presence of diagonal disorder and cavity-qubit coupling disorder. For the Tavis-Cummings model, time evolution of the photon population, the optical absorption spectra, and the hetero-entanglement between the qubits and the cavity mode are calculated by using the Green's function method to corroborate numerically exact results of Davydov's Ansätze. For the Holstein-Tavis-Cummings model, only the latter is utilized to simulate effects of disorder on the photon population dynamics and the absorption spectra. We have demonstrated that the complementary employment of analytical and numerical methods permits uncovering a fairly comprehensive picture of a variety of complex behaviors in disordered multidimensional polaritonic cavity quantum electrodynamics systems.
The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.
A nonperturbative treatment, the Dirac-Frenkel time-dependent variation is employed to examine dynamics of the Landau-Zener model with both diagonal and off-diagonal qubit-bath coupling using the multiple Davydov trial states. It is shown that steady-state transition probabilities agree with analytical predictions at long times. Landau-Zener dynamics at intermediate times is little affected by diagonal coupling, and is found to be determined by off-diagonal coupling and tunneling between two diabatic states. We investigate effects of bath spectral densities, coupling strengths, and interaction angles on Laudau-Zener dynamics. Thanks to the multiple Davydov trial states, detailed boson dynamics can also be analyzed in Landau-Zener transitions. The results presented here may help provide guiding principles to manipulate the Laudau-Zener transitions in circuit QED architectures by tuning off-diagonal coupling and tunneling strength.
The study of phase transitions in dissipative quantum systems based on the Liouvillian is often hindered by the difficulty of constructing a time-local master equation when the system-environment coupling is strong. To address this issue, the complex discretization approximation for the environment is proposed to study the quantum phase transition in the extended Jaynes-Cumming model with an infinite number of boson modes. This approach yields a non-Hermitian effective Hamiltonian that can be used to simulate the dynamics of the spin. It is found that the ground state of this effective Hamiltonian determines the spin dynamics in the single-excitation subspace. Depending on the opening of the energy gap and the maximum population of excitations on the spin degree of freedom, three distinct phases can be identified: fast decaying, localized, and stretched dynamics of the spin. This approach can be extended to multiple excitations, and similar dynamics were found in the double-excitation subspace, indicating the robustness of the single-excitation phase.
By employing the numerically accurate multiple Davydov Ansatz (mDA) formalism in combination with the thermo-field dynamics (TFD) representation of quantum mechanics, we systematically explore the influence of three parameters-temperature, photonic-mode detuning, and qubit-phonon coupling-on population dynamics and absorption spectra of the Holstein-Tavis-Cummings (HTC) model. It is found that elevated qubit-phonon couplings and/or temperatures have a similar impact on all dynamic observables: they suppress the amplitudes of Rabi oscillations in photonic populations as well as broaden the peaks and decrease their intensities in the absorption spectra. Our results unequivocally demonstrate that the HTC dynamics is very sensitive to the concerted variation of the three aforementioned parameters, and this finding can be used for fine-tuning polaritonic transport. The developed mDA-TFD methodology can be efficiently applied for modeling, predicting, optimizing, and comprehensively understanding dynamic and spectroscopic responses of actual molecular systems in microcavities.