Adiabatic terminator for fermionic hierarchical equations of motion

Abstract

The hierarchical equation of motion method has become one of the most popular numerical methods for describing the dissipative dynamics of open quantum systems linearly coupled to environment. However, its applications to systems with strong electron correlation are largely restrained by the computational cost, which is mainly caused by the high truncation tier L required to accurately characterize the strong correlation effect. In this work, we develop an adiabatic terminator by decoupling the principal dissipation mode with the fastest dissipation rate from the slower ones. The adiabatic terminator leads to substantially enhanced convergence with respect to L as demonstrated by the numerical tests carried out on a single impurity Anderson model. Moreover, the adiabatic terminator alleviates the numerical instability problems in the long-time dissipative dynamics.

Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory versus core-system hierarchy construction

“…The different structures in generalized DEOM and FP-QME can be viewed as different truncate schemes. 19 The results of the absorption spectrum using FP-QME and generalized DEOM are also shown in the Fig. 2.…”

Quantum mechanics of open systems: Dissipaton theories

“…[46][47][48][49] Various methods developed there can be directly applied; see the recent Perspective by Y. Tanimura. 42 New developments include the follows: (i ) The adiabatic terminator for hierarchy level truncation, which alleviates the numerical longtime instability problems; 76 (ii ) The time-domain Prony fitting decomposition scheme for accurate and minimum dissipaton basis set, applicable to arbitrary hybridization bath spectral densities; 63 (iii ) The implementation of matrix product state; [77][78][79][80][81][82][83] (iv ) The transformed Brownian oscillator basis; 84,85 (v ) The construction of rate kernels via DEOM by utilizing the Nakajima-Zwanzig projection techniques 86,87 and so on.…”

Unraveling the Nature of Spin Coupling in a Metal-Free Diradical: Theoretical Distinction of Ferromagnetic and Antiferromagnetic Interactions

“…To address these issues, we investigate the characteristic features in the inelastic electron tunneling spectra (IETS) of a molecular junction where the 2-OS diradical is sandwiched between two Au electrodes. We employ a first-principles-based approach that combines density functional theory (DFT) and hierarchical equations of motion (HEOM) methods − to simulate the d I /d V spectra and reproduce the experimental findings. This is followed by exploring the variations in IETS when the molecular junction undergoes mechanical stretching.…”

“…To achieve this, we utilize the above constructed AIM along with the energetic parameters extracted from the first-principles calculations. To calculate the electric current under a given bias voltage, we employ the numerically exact Fermionic HEOM method ,− , implemented in the HEOM-QUICK2 program. , The hybrid DFT+HEOM approach has been successfully applied to investigate the intricate competition between Kondo screening and spin excitation in various surface-adsorbed magnetic molecules. ,,,,, …”