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

Quantum impurity problems: Exact methods

Arne Ludwig

Prepared forJan 1, 19940 citations

Deformation of a Quantum Many-Particle System by a Rotating Impurity

Richard Schmidt, Mikhail Lemeshko

During the past 70 years, the quantum theory of angular momentum has been successfully applied to describing the properties of nuclei, atoms, and molecules, and their interactions with each other as well as with external fields.Because of the properties of quantum rotations, the angular-momentum algebra can be of tremendous complexity even for a few interacting particles, such as valence electrons of an atom, not to mention larger many-particle systems.In this work, we study an example of the latter: a rotating quantum impurity coupled to a many-body bosonic bath.In the regime of strong impurity-bath couplings, the problem involves the addition of an infinite number of angular momenta, which renders it intractable using currently available techniques.Here, we introduce a novel canonical transformation that allows us to eliminate the complex angular-momentum algebra from such a class of many-body problems.In addition, the transformation exposes the problem's constants of motion, and renders it solvable exactly in the limit of a slowly rotating impurity.We exemplify the technique by showing that there exists a critical rotational speed at which the impurity suddenly acquires one quantum of angular momentum from the many-particle bath.Such an instability is accompanied by the deformation of the phonon density in the frame rotating along with the impurity.During the past 70 years, the quantum theory of angular momentum has been successfully applied to describing the properties of nuclei, atoms, and molecules, and their interactions with each other as well as with external fields.Because of the properties of quantum rotations, the angular-momentum algebra can be of tremendous complexity even for a few interacting particles, such as valence electrons of an atom, not to mention larger many-particle systems.In this work, we study an example of the latter: a rotating quantum impurity coupled to a many-body bosonic bath.In the regime of strong impurity-bath couplings, the problem involves the addition of an infinite number of angular momenta, which renders it intractable using currently available techniques.Here, we introduce a novel canonical transformation that allows us to eliminate the complex angular-momentum algebra from such a class of many-body problems.In addition, the transformation exposes the problem's constants of motion, and renders it solvable exactly in the limit of a slowly rotating impurity.We exemplify the technique by showing that there exists a critical rotational speed at which the impurity suddenly acquires one quantum of angular momentum from the many-particle bath.Such an instability is accompanied by the deformation of the phonon density in the frame rotating along with the impurity.

arXiv:1507.03987Physical Review XFeb 12, 201669 citations

New Exact Results for Quantum Impurity Problems

Frédéric Lesage, Hubert Saleur, P. Simonetti

Springer eBooksJan 1, 20000 citations

Generalized Wilson chain for solving multichannel quantum impurity problems

Andrew K. Mitchell, Martin R. Galpin, Samuel Wilson-Fletcher +2 more

The numerical renormalization group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within dynamical mean field theory. Here we present a simple generalization of the Wilson chain, which improves the scaling of computational cost with the number of conduction bands, bringing more complex problems within reach. The method is applied to calculate the $t$ matrix of the three-channel Kondo model at $T=0$ , which shows universal crossovers near non-Fermi-liquid critical points. A nonintegrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening and overscreening mechanisms.The numerical renormalization group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within dynamical mean field theory. Here we present a simple generalization of the Wilson chain, which improves the scaling of computational cost with the number of conduction bands, bringing more complex problems within reach. The method is applied to calculate the $t$ matrix of the three-channel Kondo model at $T=0$, which shows universal crossovers near non-Fermi-liquid critical points. A nonintegrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening and overscreening mechanisms.

arXiv:1308.1903Physical Review BMar 12, 201465 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.

t

matrix of the three-channel Kondo model at

T=0

, which shows universal crossovers near non-Fermi-liquid critical points. A nonintegrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening and overscreening mechanisms.