Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model

doi:10.1088/1674-1056/ada54f

中国物理B ›› 2025, Vol. 34 ›› Issue (2): 27102-027102.doi: 10.1088/1674-1056/ada54f

Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model

Hou-Min Du(杜厚旻) and Yu-Liang Liu(刘玉良)†

Department of Physics, Renmin University of China, Beijing 100872, China

收稿日期:2024-11-05 修回日期:2024-12-31 接受日期:2025-01-03 出版日期:2025-02-15 发布日期:2025-01-15
通讯作者: Yu-Liang Liu E-mail:ylliu@ruc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11974420).

Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model

Hou-Min Du(杜厚旻) and Yu-Liang Liu(刘玉良)†

Department of Physics, Renmin University of China, Beijing 100872, China

Received:2024-11-05 Revised:2024-12-31 Accepted:2025-01-03 Online:2025-02-15 Published:2025-01-15
Contact: Yu-Liang Liu E-mail:ylliu@ruc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11974420).

摘要/Abstract

摘要： Understanding the quantum critical phenomena is one of the most important and challenging tasks in condensed matter physics and the two-impurity Anderson model (TIAM) is a good starting point for this exploration. To this end, we employ the algebraic equation of motion approach to calculate the TIAM and analytically obtain the explicit single-particle impurity Green function under the soft cut-off approximation (SCA). This approach effectively incorporates the impurity spacing as an intrinsic parameter. By solving the pole equations of the Green function, we have, for the first time, qualitatively calculated the spectral weight functions of the corresponding low-energy excitations. We find that when the impurity spacing is less than one lattice distance, the dynamic Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction effectively enters, resulting in a rapid increase in the spectral weights of the RKKY phase, which ultimately surpass those of the Kondo phase; while the spectral weights of the Kondo phase are strongly suppressed. From the perspective of spectral weights, we further confirm the existence of a crossover from the Kondo phase to the RKKY phase in the TIAM. Based on these results, the reasons for the phenomenon of the Kondo resonance splitting are also discussed.

关键词: multiple-point correlation function, soft cut-off approximation, Kondo resonance splitting, RKKY interaction

Abstract: Understanding the quantum critical phenomena is one of the most important and challenging tasks in condensed matter physics and the two-impurity Anderson model (TIAM) is a good starting point for this exploration. To this end, we employ the algebraic equation of motion approach to calculate the TIAM and analytically obtain the explicit single-particle impurity Green function under the soft cut-off approximation (SCA). This approach effectively incorporates the impurity spacing as an intrinsic parameter. By solving the pole equations of the Green function, we have, for the first time, qualitatively calculated the spectral weight functions of the corresponding low-energy excitations. We find that when the impurity spacing is less than one lattice distance, the dynamic Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction effectively enters, resulting in a rapid increase in the spectral weights of the RKKY phase, which ultimately surpass those of the Kondo phase; while the spectral weights of the Kondo phase are strongly suppressed. From the perspective of spectral weights, we further confirm the existence of a crossover from the Kondo phase to the RKKY phase in the TIAM. Based on these results, the reasons for the phenomenon of the Kondo resonance splitting are also discussed.

Key words: multiple-point correlation function, soft cut-off approximation, Kondo resonance splitting, RKKY interaction

中图分类号: (Theories and models; localized states)

71.23.An

75.30.Hx (Magnetic impurity interactions) 03.65.Fd (Algebraic methods)

Hou-Min Du(杜厚旻) and Yu-Liang Liu(刘玉良). Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model[J]. 中国物理B, 2025, 34(2): 27102-027102.

Hou-Min Du(杜厚旻) and Yu-Liang Liu(刘玉良). Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model[J]. Chin. Phys. B, 2025, 34(2): 27102-027102.

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Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model

Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model

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