Coherent interaction and action-counteraction theory in small polaron systems, and ground state properties

doi:10.1088/1674-1056/ac67c1

中国物理B ›› 2022, Vol. 31 ›› Issue (11): 117104-117104.doi: 10.1088/1674-1056/ac67c1

Coherent interaction and action-counteraction theory in small polaron systems, and ground state properties

Zhi-Hua Luo(罗质华)^† and Chao-Fan Yu(余超凡)

School of Physics and Information Engineering, Guangdong University of Education, Guangzhou 510303, China

收稿日期:2021-11-29 修回日期:2021-11-29 接受日期:2022-04-18 出版日期:2022-10-17 发布日期:2022-10-17
通讯作者: Zhi-Hua Luo E-mail:lo-zh@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10574163).

Coherent interaction and action-counteraction theory in small polaron systems, and ground state properties

Zhi-Hua Luo(罗质华)^† and Chao-Fan Yu(余超凡)

School of Physics and Information Engineering, Guangdong University of Education, Guangzhou 510303, China

Received:2021-11-29 Revised:2021-11-29 Accepted:2022-04-18 Online:2022-10-17 Published:2022-10-17
Contact: Zhi-Hua Luo E-mail:lo-zh@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10574163).

摘要/Abstract

摘要： Based on the coherent interaction and action-counteraction principles, we investigate the ground state properties for small polaron systems, the coherent-squeezed fluctuation correction, and the anomalous lattice quantum fluctuation, with the new variational generator containing correlated squeezed-coherent coupling and quantum entanglement. Noting that $-2t $ is the T.B.A. energy, for the coherent interaction effect, we find the ground-state energy $E_0$ to be $-2.428t$, in which the coherent squeezed fluctuation correction $-A_0 t$ is $-0.463t $ (where $ t $ is the hopping integral, $\omega $ is the phonon frequency), with the electron-one-phonon coupling constant $g=$1 and the electron-two-phonon coupling constant $g_{1}=-0.1$. However, as a result of the action-counteraction effect, $\tilde{{E}}_{0} $ is $-2.788t$, but $-\tilde{{A}}_{0} t$ is $-0.735t$. As to the polaron binding energy $(E_{\rm P} )$, for the coherent interaction effect, $E_{\rm P} $ is $-1.38\omega $, but for the action-counteraction effect, $\tilde{{E}}_{\rm P}$ is $-1.88\omega $. In particular, the electron-two-phonon interaction noticeably enlarges the coherent interaction and the coherent squeezed quantum fluctuation correction. By intervening with the quantum entanglement, the evolutions of the squeezed coherent state and the lattice quantum fluctuation begin to take control. At that time, we encounter a new quantum phase coherence phenomenon — the collapse and revival of inversion repeatedly for the coherent state in the entangled evolution.

关键词: coherent interaction and action-counteraction, correlated representation variational approach, entangled-squeezed coherent state, interaction of electron with the coherent squeezed fluctuation

Abstract: Based on the coherent interaction and action-counteraction principles, we investigate the ground state properties for small polaron systems, the coherent-squeezed fluctuation correction, and the anomalous lattice quantum fluctuation, with the new variational generator containing correlated squeezed-coherent coupling and quantum entanglement. Noting that $-2t $ is the T.B.A. energy, for the coherent interaction effect, we find the ground-state energy $E_0$ to be $-2.428t$, in which the coherent squeezed fluctuation correction $-A_0 t$ is $-0.463t $ (where $ t $ is the hopping integral, $\omega $ is the phonon frequency), with the electron-one-phonon coupling constant $g=$1 and the electron-two-phonon coupling constant $g_{1}=-0.1$. However, as a result of the action-counteraction effect, $\tilde{{E}}_{0} $ is $-2.788t$, but $-\tilde{{A}}_{0} t$ is $-0.735t$. As to the polaron binding energy $(E_{\rm P} )$, for the coherent interaction effect, $E_{\rm P} $ is $-1.38\omega $, but for the action-counteraction effect, $\tilde{{E}}_{\rm P}$ is $-1.88\omega $. In particular, the electron-two-phonon interaction noticeably enlarges the coherent interaction and the coherent squeezed quantum fluctuation correction. By intervening with the quantum entanglement, the evolutions of the squeezed coherent state and the lattice quantum fluctuation begin to take control. At that time, we encounter a new quantum phase coherence phenomenon — the collapse and revival of inversion repeatedly for the coherent state in the entangled evolution.

Key words: coherent interaction and action-counteraction, correlated representation variational approach, entangled-squeezed coherent state, interaction of electron with the coherent squeezed fluctuation

中图分类号: (Polarons and electron-phonon interactions)

71.38.-k

71.38.Mx (Bipolarons) 71.45.Lr (Charge-density-wave systems) 71.30.+h (Metal-insulator transitions and other electronic transitions)

Zhi-Hua Luo(罗质华) and Chao-Fan Yu(余超凡). Coherent interaction and action-counteraction theory in small polaron systems, and ground state properties[J]. 中国物理B, 2022, 31(11): 117104-117104.

Zhi-Hua Luo(罗质华) and Chao-Fan Yu(余超凡). Coherent interaction and action-counteraction theory in small polaron systems, and ground state properties[J]. Chin. Phys. B, 2022, 31(11): 117104-117104.

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Coherent interaction and action-counteraction theory in small polaron systems, and ground state properties

Coherent interaction and action-counteraction theory in small polaron systems, and ground state properties

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