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

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, many-body 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. WIREs Comput Mol Sci 2016, 6:608–638. doi: 10.1002/wcms.1269 For further resources related to this article, please visit the WIREs website.