A continuous-time solver for quantum impurity models

We present a new continuous time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons to quantum Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.Comment: Published versio

Benchmarking a semiclassical impurity solver for dynamical-mean-field theory: self-energies and magnetic transitions of the single-orbital Hubbard model

An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to the correlated-electron models. The method is based on performing a exact numerical integral over the zero-Matsubara-frequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descents treatment of the charge part. We test this method by applying it to one or two site approximations to the single band Hubbard model with different band structures, and comparing the results to quantum Monte-Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states and magnetic transition temperatures show reasonable agreement with the quantum Monte-Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.Comment: 14 pages, 15 figure