Scaling analysis of SU(4) kondo effect and dynamics of entanglement

We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a ${T}^{2}$ coefficient of conductance becomes zero at quarter-filling, whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$ . We find that the conductance shows the SU(4) scaling behavior at ${\ensuremath{\mu}}_{B}B<{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$ and it exhibits the SU(2) universality at ${\ensuremath{\mu}}_{B}B\ensuremath{\gg}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$, where ${T}_{K}^{\mathrm{SU}(4)}$ is the SU(4) Kondo temperature. To clarify how the excited states evolve along the SU(4) to SU(2) crossover, we also calculate the spectral function. The results show that the Kondo resonance width of the two states locked at the Fermi level becomes sharper with increasing fields. The spectral peaks of the other two levels moving away from the Fermi level merge with atomic limit peaks for ${\ensuremath{\mu}}_{B}B\ensuremath{\gtrsim}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$.We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a ${T}^{2}$ coefficient of conductance becomes zero at quarter-filling, whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$. We find that the conductance shows the SU(4) scaling behavior at ${\ensuremath{\mu}}_{B}B<{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$ and it exhibits the SU(2) universality at ${\ensuremath{\mu}}_{B}B\ensuremath{\gg}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$, where ${T}_{K}^{\mathrm{SU}(4)}$ is the SU(4) Kondo temperature. To clarify how the excited states evolve along the SU(4) to SU(2) crossover, we also calculate the spectral function. The results show that the Kondo resonance width of the two states locked at the Fermi level becomes sharper with increasing fields. The spectral peaks of the other two levels moving away from the Fermi level merge with atomic limit peaks for ${\ensuremath{\mu}}_{B}B\ensuremath{\gtrsim}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$.

arXiv:2003.12715Physical review. B./Physical review. BOct 6, 202017 citations

Probing the Kondo Regime with Entanglement Measures

Abolfazl Bayat, Pasquale Sodano, Sougato Bose

Apr 21, 20091 citation

Multistage Kondo effect as a manifestation of dynamical symmetries in the single- and two-electron tunneling

K. Kikoin

The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction $U$ . It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU(4) dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 1/2 in the positive $U$ model and the Kondo resonance for pair tunneling in the negative $U$ model is a direct manifestation of implicit SU(4) symmetry of the Anderson/Kondo model.The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction $U$. It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU(4) dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 1/2 in the positive $U$ model and the Kondo resonance for pair tunneling in the negative $U$ model is a direct manifestation of implicit SU(4) symmetry of the Anderson/Kondo model.

arXiv:1108.5121Aug 25, 20110 citations

T

can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a

{T}^{2}

coefficient of conductance becomes zero at quarter-filling, whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields

B

. We find that the conductance shows the SU(4) scaling behavior at ${\ensuremath{\mu}}_{B}B<{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$ and it exhibits the SU(2) universality at ${\ensuremath{\mu}}_{B}B\ensuremath{\gg}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$, where

{T}_{K}^{\mathrm{SU}(4)}

is the SU(4) Kondo temperature. To clarify how the excited states evolve along the SU(4) to SU(2) crossover, we also calculate the spectral function. The results show that the Kondo resonance width of the two states locked at the Fermi level becomes sharper with increasing fields. The spectral peaks of the other two levels moving away from the Fermi level merge with atomic limit peaks for ${\ensuremath{\mu}}_{B}B\ensuremath{\gtrsim}{k}_{B}{T}_{K}^{\mathrm{SU}(4)}$.

The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction

U

. It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU(4) dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 1/2 in the positive

U

model and the Kondo resonance for pair tunneling in the negative

U

model is a direct manifestation of implicit SU(4) symmetry of the Anderson/Kondo model.