Hierarchical equations of motion approach for accurate characterization of spin excitations in quantum impurity systems

Abstract

Recent technological advancement in scanning tunneling microscope has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments, and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.

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. ,,,,, …”