Nanoscale physics and dynamical mean-field theory have both generated increased interest in complex quantum impurity problems and so have focused attention on the need for flexible quantum impurity solvers. Here we demonstrate that the mapping of single-quantum impurity problems onto spin chains can be exploited to yield a powerful and extremely flexible impurity solver. We implement this cluster algorithm explicitly for the Anderson and Kondo Hamiltonians, and illustrate its use in the ``mesoscopic Kondo problem.'' To study universal Kondo physics, a large ratio between the effective bandwidth ${D}_{\mathrm{eff}}$ and the temperature $T$ is required; our cluster algorithm treats the mesoscopic fluctuations exactly while being able to approach the large ${D}_{\mathrm{eff}}∕T$ limit with ease. We emphasize that the flexibility of our method allows it to tackle a wide variety of quantum impurity problems; thus, it may also be relevant to the dynamical mean-field theory of lattice problems.Nanoscale physics and dynamical mean-field theory have both generated increased interest in complex quantum impurity problems and so have focused attention on the need for flexible quantum impurity solvers. Here we demonstrate that the mapping of single-quantum impurity problems onto spin chains can be exploited to yield a powerful and extremely flexible impurity solver. We implement this cluster algorithm explicitly for the Anderson and Kondo Hamiltonians, and illustrate its use in the ``mesoscopic Kondo problem.'' To study universal Kondo physics, a large ratio between the effective bandwidth ${D}_{\mathrm{eff}}$ and the temperature $T$ is required; our cluster algorithm treats the mesoscopic fluctuations exactly while being able to approach the large ${D}_{\mathrm{eff}}∕T$ limit with ease. We emphasize that the flexibility of our method allows it to tackle a wide variety of quantum impurity problems; thus, it may also be relevant to the dynamical mean-field theory of lattice problems.

arXiv:cond-mat/0411313Physical Review BMay 27, 200516 citations

Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations

Eitan Eidelstein, Emanuel Gull, Guy Cohen

We present a numerically exact inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems.We present a numerically exact inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems.

arXiv:1907.08570Physical Review LettersMay 22, 202037 citations

{D}_{\mathrm{eff}}

and the temperature

T

is required; our cluster algorithm treats the mesoscopic fluctuations exactly while being able to approach the large

{D}_{\mathrm{eff}}∕T

limit with ease. We emphasize that the flexibility of our method allows it to tackle a wide variety of quantum impurity problems; thus, it may also be relevant to the dynamical mean-field theory of lattice problems.