Numerical renormalization group study of the two-channel Kondo model

We perform numerical renormalization group (NRG) as well as analytical calculations for the two-channel Kondo (2CK) model to obtain the dependence of the Kondo temperature ${T}_{K}$ on the dimensionless (bare) spin exchange coupling $g$ over the complete parameter range from $g⪡1$ to $g⪢1$ . We show that there exists a duality between the regimes of small and large coupling. It is unique for the two-channel model and enables a mapping between the strong and the weak coupling cases via the identification $g\ensuremath{\leftrightarrow}3∕(2g)$, implying an exponential dependence of ${T}_{K}$ on $1∕g$ and $g$ , respectively, in the two regimes. This agrees quantitatively with our NRG calculations where we extract ${T}_{K}(g)$ over the complete parameter range and obtain a nonmonotonic ${T}_{K}(g)$ dependence, strongly peaked at the 2CK fixed point coupling ${g}^{*}$ . These results may be relevant for resolving the long-standing puzzle within the 2CK interpretation of certain random defect systems as to why no broad distribution of ${T}_{K}$ is observed in those systems.We perform numerical renormalization group (NRG) as well as analytical calculations for the two-channel Kondo (2CK) model to obtain the dependence of the Kondo temperature ${T}_{K}$ on the dimensionless (bare) spin exchange coupling $g$ over the complete parameter range from $g⪡1$ to $g⪢1$. We show that there exists a duality between the regimes of small and large coupling. It is unique for the two-channel model and enables a mapping between the strong and the weak coupling cases via the identification $g\ensuremath{\leftrightarrow}3∕(2g)$, implying an exponential dependence of ${T}_{K}$ on $1∕g$ and $g$, respectively, in the two regimes. This agrees quantitatively with our NRG calculations where we extract ${T}_{K}(g)$ over the complete parameter range and obtain a nonmonotonic ${T}_{K}(g)$ dependence, strongly peaked at the 2CK fixed point coupling ${g}^{*}$. These results may be relevant for resolving the long-standing puzzle within the 2CK interpretation of certain random defect systems as to why no broad distribution of ${T}_{K}$ is observed in those systems.

arXiv:cond-mat/0610631Physical Review BJan 26, 200716 citations

Perturbative renormalization of multi-channel Kondo-type models

Yoshio Kuramoto

arXiv:cond-mat/9805009The European Physical Journal BOct 1, 199820 citations

Numerical renormalization group method for quantum impurity systems

R. Bulla, Theo A. Costi, Thomas Pruschke

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.

arXiv:cond-mat/0701105Reviews of Modern PhysicsApr 2, 20081,475 citations

Low-temperature physics of the two-impurity, two-channel Kondo model

Kevin Ingersent, Barbara Jones

Physica B Condensed MatterApr 1, 19947 citations

We perform numerical renormalization group (NRG) as well as analytical calculations for the two-channel Kondo (2CK) model to obtain the dependence of the Kondo temperature

{T}_{K}

on the dimensionless (bare) spin exchange coupling

g

over the complete parameter range from

g⪡1

g⪢1

. We show that there exists a duality between the regimes of small and large coupling. It is unique for the two-channel model and enables a mapping between the strong and the weak coupling cases via the identification $g\ensuremath{\leftrightarrow}3∕(2g)$, implying an exponential dependence of

{T}_{K}

1∕g

and

g

, respectively, in the two regimes. This agrees quantitatively with our NRG calculations where we extract

{T}_{K}(g)

over the complete parameter range and obtain a nonmonotonic

{T}_{K}(g)

dependence, strongly peaked at the 2CK fixed point coupling

{g}^{*}

. These results may be relevant for resolving the long-standing puzzle within the 2CK interpretation of certain random defect systems as to why no broad distribution of

{T}_{K}

is observed in those systems.