Efficient variational approach to the impurity problem and its application to the dynamical mean-field theory

TL;DR

This paper introduces an efficient variational method based on configuration interaction expansion to solve the Anderson impurity problem, significantly reducing computational complexity and enabling practical applications within dynamical mean-field theory.

Contribution

The paper presents a novel variational approach that achieves accurate ground states with much smaller matrices, improving the efficiency of impurity solvers in dynamical mean-field theory.

Findings

Accurate ground states obtained with less than 10% of full Hamiltonian dimension.

Demonstrated application to the attractive Hubbard model with superconducting solutions.

Enhanced efficiency of impurity problem solutions in dynamical mean-field theory.

Abstract

Within the framework of exact diagonalization (ED), we compute the ground state of Anderson impurity problem using the variational approach based on the configuration interaction (CI) expansion. We demonstrate that an accurate ground state can be obtained by iteratively diagonalizing a matrix with the dimension that is less than 10$%$ of the full Hamiltonian. The efficiency of the CI expansion for different problems is analyzed. By way of example, we apply this method to the single-site dynamical mean field theory using ED as the impurity solver. Specifically, to demonstrate the usefulness of this approach, we solve the attractive Hubbard model in the grand-canonical ensemble, where the s-wave superconducting solution is explicitly obtained.