Abstract
We present a diagrammatic Monte Carlo method for quantum impurity problems with general interactions and general hybridization functions. Our method uses a recursive determinant scheme to sample diagrams for the scattering amplitude. Unlike in other methods for general impurity problems, an approximation of the continuous hybridization function by a finite number of bath states is not needed, and accessing low temperature does not incur an exponential cost. We test the method for the example of molecular systems, where we systematically vary temperature, interatomic distance, and basis set size. We further apply the method to an impurity problem generated by a self-energy embedding calculation of correlated antiferromagnetic NiO. We find that the method is ideal for quantum impurity problems with a large number of orbitals but only moderate correlations.
Highlights
Quantum impurity models, originally introduced to describe magnetic impurities such as iron or copper atoms with partially filled d shells in a nonmagnetic host material [1], have since found applications in nanoscience as representations of quantum dots and molecular conductors [2] and in surface science to understand the adsorption of atoms on surfaces [3,4]
While the original formulation of a quantum impurity model [1] only describes a single correlated orbital coupled to a noninteracting environment, in general the impurities occurring in the context of surface science and embedding theories contain many orbitals with general four-fermion interactions and few symmetries [24]
Since the kinetic energy of electrons moving between two atoms is significantly reduced as we increase r but the longrange Coulomb repulsion between electrons changes slowly, the electron-electron interaction becomes more important at larger r, and it is expected that the perturbation expansion becomes more difficult to converge
Summary
Originally introduced to describe magnetic impurities such as iron or copper atoms with partially filled d shells in a nonmagnetic host material [1], have since found applications in nanoscience as representations of quantum dots and molecular conductors [2] and in surface science to understand the adsorption of atoms on surfaces [3,4] They form the central part of embedding theories such as the dynamical mean-field theory (DMFT) [5,6] and its variants [7,8,9,10,11,12,13,14,15,16,17,18,19], as well as the self-energy embedding theory (SEET) [20,21,22], where they describe the behavior of a few “strongly correlated” orbitals embedded into a weakly correlated or noninteracting background of other orbitals. Hamiltonian-based methods, such as exact diagonalization (ED) [25,26,27,28,29] and its variants [30], configuration-interactions [31], or coupled
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