Inchworm tensor train hybridization expansion quantum impurity solver

TL;DR

This paper introduces a tensor train-based approach to improve the accuracy and efficiency of quantum impurity solvers, especially for complex multi-orbital systems, by integrating it with the inchworm hybridization expansion method.

Contribution

It presents a novel combination of tensor train methods with the inchworm hybridization expansion to enhance quantum impurity problem solutions.

Findings

Tensor train methods improve solver accuracy for multi-orbital systems.

The approach efficiently handles complex hybridizations and interactions.

Results demonstrate the method's versatility and potential for condensed matter applications.

Abstract

The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing accurate results for multi-orbital systems with complex interactions and off-diagonal hybridizations. Recently, tensor-train-based integration and summation techniques have shown promise as effective alternatives. In this study, we use tensor train methods to tackle quantum impurity problems formulated within the imaginary-time inchworm hybridization expansion framework. We identify key challenges in the inchworm expansion itself and its interplay with tensor-train-based methods. We demonstrate the accuracy and versatility of our approach by solving general quantum impurity problems. Our results suggest that tensor-train decomposition schemes offer a viable path toward accurate and efficient multi-orbital impurity solvers.