Numerical Renormalization Group Study of Quadrupole Kondo Effect with the Crystal-field Excited State
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| Format: | Preprint |
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2023
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| author | Kaneko, Yuki Tsunetsugu, Hirokazu |
| author_facet | Kaneko, Yuki Tsunetsugu, Hirokazu |
| contents | We have studied the quadrupolar Kondo effect for an impurity in cubic environment with taking account of a singlet excited state $Γ_1$, which models a $\mathrm{Pr}^{3+}$ ion with a non-Kramers double ground state $Γ_3$. We have used the numerical renormalization group approach and determined the phase diagram with varying quadrupole Kondo coupling $J$ and $Γ_1$ excitation energy $Δ$. Two phases are found and identified as local Fermi liquid and non-Fermi liquid. This non-Fermi liquid phase is characteristic to the two-channel Kondo impurity, and a similar phase diagram has been also found in other extended quadrupole models. We have analyzed in detail the $J$-dependence of the Kondo temperature $T_K$ near the phase boundary $J_c (Δ) $ and found a nice scaling behavior with an stretched exponential form $T_K \sim δJ^α \exp (-\mathrm{const.}/\sqrt{δJ})$ where $δJ \equiv J - J_c (Δ)$. This differs from the standard scaling form and indicates that one needs to consider renormalization of multiple coupling constants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_15936 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Numerical Renormalization Group Study of Quadrupole Kondo Effect with the Crystal-field Excited State Kaneko, Yuki Tsunetsugu, Hirokazu Strongly Correlated Electrons We have studied the quadrupolar Kondo effect for an impurity in cubic environment with taking account of a singlet excited state $Γ_1$, which models a $\mathrm{Pr}^{3+}$ ion with a non-Kramers double ground state $Γ_3$. We have used the numerical renormalization group approach and determined the phase diagram with varying quadrupole Kondo coupling $J$ and $Γ_1$ excitation energy $Δ$. Two phases are found and identified as local Fermi liquid and non-Fermi liquid. This non-Fermi liquid phase is characteristic to the two-channel Kondo impurity, and a similar phase diagram has been also found in other extended quadrupole models. We have analyzed in detail the $J$-dependence of the Kondo temperature $T_K$ near the phase boundary $J_c (Δ) $ and found a nice scaling behavior with an stretched exponential form $T_K \sim δJ^α \exp (-\mathrm{const.}/\sqrt{δJ})$ where $δJ \equiv J - J_c (Δ)$. This differs from the standard scaling form and indicates that one needs to consider renormalization of multiple coupling constants. |
| title | Numerical Renormalization Group Study of Quadrupole Kondo Effect with the Crystal-field Excited State |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2312.15936 |