Hierarchical equations of motion for an impurity solver in dynamical mean-field theory

Abstract

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly correlated electronic systems, in the framework of dynamical mean-field theory (DMFT). The HEOM method is also numerically convenient to achieve the same level of accuracy as that using the state-of-the-art numerical renormalization group impurity solver at finite temperatures. The practicality of the HEOM+DMFT method is demonstrated by its applications to the Hubbard models with Bethe and hypercubic lattice structures. We investigate the metal-insulator transition phenomena, and address the effects of temperature on the properties of strongly correlated lattice systems.

Thermopower of few-electron quantum dots with Kondo correlations

“…[51,54]. Figure 4 clearly affirms that the HEOM approach can accurately capture the Kondo spectral peaks at a relatively low L.…”

“…[51][52][53][54]. In particular, the correct Kondo scaling behavior and the analytic logarithmic Kondo tail have been recovered with the HEOM calculations [51].…”

“…A number of numerical approaches have been employed to study strongly correlated QDs. These include the numerical renormalization group approach [38][39][40][41], the quantum Monte Carlo approach [42,43], the exact diagonalization approach [44,45], the noncrossing approximation [46,47], and the hierarchical equations of motion (HEOM) approach [48][49][50][51][52][53][54]. In this paper, we employ the HEOM approach to investigate the thermoelectric properties of single-and two-level QDs.…”

Current noise spectra and mechanisms with dissipaton equation of motion theory

“…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.…”

“…These include the studies of transient electronic transport, [27][28][29][30] thermopower, 31 and the spectral density of local impurity system in the Kondo regime. 32,33 The HEOM approach has also been used as an impurity solver 34 in the context of dynamical mean-field theory. 35 However, the original HEOM formalism does not explicitly address the hybridizing bath dynamics, due to its path-integral influence functionalbased construction.…”