Improving the efficiency of hierarchical equations of motion approach and application to coherent dynamics in Aharonov–Bohm interferometers

Hou, Dong; Wang, Shikuan; Wang, Rulin; Ye, LvZhou; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

doi:10.1063/1.4914514

Cited by 52 publications

(58 citation statements)

References 68 publications

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“…As long as the numerical convergence is reached, the results are guaranteed to be quantitatively accurate. [32][33][34]43 The minimal truncation tier L required to achieve convergence is closely dependent on the configurations of system as well as bath. Energetic properties such as the strength of electron correlation, the system-reservoir coupling, and the temperature will all have influence on L. It is difficult to have an a priori estimation for the required minimal L. In practice, the convergence with respect to L is tested case by case.…”

Section: A Numerical Implementation Of Deommentioning

confidence: 99%

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Current noise spectra and mechanisms with dissipaton equation of motion theory

Jin

Wang

Zheng

et al. 2015

The Journal of Chemical Physics

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Based on the Yan's dissipaton equation of motion (DEOM) theory [J. Chem. Phys. 140, 054105 (2014)], we investigate the characteristic features of current noise spectrum in several typical transport regimes of a single-impurity Anderson model. Many well-known features such as Kondo features are correctly recovered by our DEOM calculations. More importantly, it is revealed that the intrinsic electron cotunneling process is responsible for the characteristic signature of current noise at anti-Stokes frequency. We also identify completely destructive interference in the noise spectra of noninteracting systems with two degenerate transport channels.

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Section: A Numerical Implementation Of Deommentioning

confidence: 99%

“…For simplicity, we assume further that the poles of hybridization function do not have explicit dependence on the system spin-orbital. 43 Dissipaton decomposition for the hybridizing bath thus reads…”

Section: Dissipaton Description Of Bath and Generalized Diffusionmentioning

confidence: 99%

Current noise spectra and mechanisms with dissipaton equation of motion theory

Jin

Wang

Zheng

et al. 2015

The Journal of Chemical Physics

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“…10−13 To treat the entire system quantum mechanically in a consistent and rigorous fashion, we have to expand the scope of the Hamiltonian, eq 17, by including the coupling to the surrounding environment represented by eq 1 with eq 2. Here, we chose the system part of system-bath interaction 18) which indicates that all spins interact with the single bath system. Then, for spectral distribution, eq 2, non-Markovian and nonperturbative dynamics of the reduced system can be studied by integrating the HEOM, eqs 3−6.…”

Section: Dynamics Of Quantum Spin Glass Systemmentioning

confidence: 99%

Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach Using a Graphics Processing Unit (GPU)

Tsuchimoto

Tanimura

2015

J. Chem. Theory Comput.

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A system with many energy states coupled to a harmonic oscillator bath is considered. To study quantum non-Markovian system-bath dynamics numerically rigorously and nonperturbatively, we developed a computer code for the reduced hierarchy equations of motion (HEOM) for a graphics processor unit (GPU) that can treat the system as large as 4096 energy states. The code employs a Padé spectrum decomposition (PSD) for a construction of HEOM and the exponential integrators. Dynamics of a quantum spin glass system are studied by calculating the free induction decay signal for the cases of 3 × 2 to 3 × 4 triangular lattices with antiferromagnetic interactions. We found that spins relax faster at lower temperature due to transitions through a quantum coherent state, as represented by the off-diagonal elements of the reduced density matrix, while it has been known that the spins relax slower due to suppression of thermal activation in a classical case. The decay of the spins are qualitatively similar regardless of the lattice sizes. The pathway of spin relaxation is analyzed under a sudden temperature drop condition. The Compute Unified Device Architecture (CUDA) based source code used in the present calculations is provided as Supporting Information .

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“…This means that, to achieve a preset accuracy, the minimally required P increases as the temperature is lowered. A quantitative estimate of P has been proposed as follows:

normalln P = 1.10 normalln ((), prefix- 0.28 normalln E_{c}) - 0.50 normalln ((), \frac{T}{W})

…”

Section: Heom‐quick: Numerical Algorithms and Techniquesmentioning

confidence: 99%

“…The sparsity feature is completely determined by the system Hamiltonian H sys and the reservoir spectral functions

J_{α s v v^{'}} ((), ω)

. Two ansatzs have been proposed to quickly identify and screen out the zero elements of ADOs . First, the sparsity of ρ (0) is determined by an effective Hamiltonian

H_{eff} = H_{normals normaly normals} + H_{normals normaly normals}^{'} + H_{Σ}

via

ρ^{(0)} \sim e^{prefix- β H_{eff}}

.…”

Section: Heom‐quick: Numerical Algorithms and Techniquesmentioning

confidence: 99%

HEOM‐QUICK: a program for accurate, efficient, and universal characterization of strongly correlated quantum impurity systems

Wang

Hou

et al. 2016

WIREs Comput Mol Sci

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116

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Accurate characterization of correlated electronic states, as well as their evolution under external fields or in dissipative environment, is essentially important for understanding the properties of strongly correlated transition-metal materials involving spin-unpaired d or f electrons. This paper reviews the development and applications of a numerical simulation program, the Hierarchical Equations of Motion for QUantum Impurity with a Correlated Kernel (HEOM-QUICK), which allows for an accurate and universal characterization of strongly correlated quantum impurity systems. The HEOM-QUICK program implements the formally exact HEOM formalism for fermionic open systems. Its simulation results capture the combined effects of system-environment dissipation, manybody interactions, and non-Markovian memory in a nonperturbative manner. The HEOM-QUICK program has been employed to explore a wide range of static and dynamic properties of various types of quantum impurity systems, including charge or spin qubits, quantum dots, molecular junctions, and so on. It has also been utilized in conjunction with first-principles methods such as density-functional theory methods to study the correlated electronic structure of adsorbed magnetic molecules. The advantages in its accuracy, efficiency, and universality have made the HEOM-QUICK program a reliable and versatile tool for theoretical investigations on strong electron correlation effects in complex materials.

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Improving the efficiency of hierarchical equations of motion approach and application to coherent dynamics in Aharonov–Bohm interferometers

Cited by 52 publications

References 68 publications

Current noise spectra and mechanisms with dissipaton equation of motion theory

Current noise spectra and mechanisms with dissipaton equation of motion theory

Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach Using a Graphics Processing Unit (GPU)

HEOM‐QUICK: a program for accurate, efficient, and universal characterization of strongly correlated quantum impurity systems

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