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

TL;DR

This paper introduces a nonperturbative hierarchical equations of motion (HEOM) impurity solver for dynamical mean-field theory, providing accurate and computationally efficient analysis of strongly correlated electronic systems at finite temperatures.

Contribution

It develops a novel HEOM-based impurity solver that achieves high accuracy and numerical convenience within DMFT, applicable to complex lattice models.

Findings

Accurately evaluates physical properties of strongly correlated systems.

Effectively captures metal-insulator transition phenomena.

Demonstrates temperature effects on lattice system properties.

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 novel 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.