[论文解读] Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result

Severino Adler, Friedrich Krien+3 more|arXiv (Cornell University)|Dec 19, 2022

Quantum and electron transport phenomena参考文献 77被引用 6

一句话总结

本文通过单玻色子交换（SBE）形式化方法分解广义局域电荷磁化率，揭示了关联电子系统中非微扰自旋-电荷关联纠缠的微观起源。研究发现，Matsubara频率空间中的对角抑制源于电子与寿命更长、耦合增强的局域磁矩的散射，而非对角增强则源于多玻色子过程。Kondo效应在低温下削弱了自旋-电荷纠缠，阐明了在平均场理论之外微扰理论失效的原因。

ABSTRACT

We study the microscopic mechanism controlling the interplay between local charge and local spin fluctuations in correlated electron systems via a thorough investigation of the generalized on-site charge susceptibility of several fundamental many-electron models, such as the Hubbard atom, the Anderson impurity model, and the Hubbard model. By decomposing the numerically determined generalized susceptibility in terms of physically transparent single-boson exchange processes, we unveil the microscopic mechanisms responsible for the breakdown of the self-consistent many-electron perturbation expansion. In particular, we unambiguously identify the origin of the significant suppression of its diagonal entries in (Matsubara) frequency space and the slight increase of the off-diagonal ones which cause the breakdown. The suppression effect on the diagonal elements originates directly from the electronic scattering on local magnetic moments, reflecting their increasingly longer lifetime as well as their enhanced effective coupling with the electrons. Instead, the slight and diffuse enhancement of the off-diagonal terms can be mostly ascribed to multiboson scattering processes. The strong intertwining between spin and charge sectors is partly weakened at the Kondo temperature due to a progressive reduction of the effective spin-fermion coupling of local magnetic fluctuations in the low frequency regime. Our analysis, thus, clarifies the precise mechanism through which the physical information is transferred between different scattering channels of interacting electron problems and highlights the pivotal role played by such an intertwining in the physics of correlated electrons beyond the perturbative regime.

研究动机与目标

• 识别关联体系中自洽多体微扰理论失效的微观机制。
• 阐明Matsubara频率空间中广义电荷磁化率矩阵对角项抑制与非对角项增强的物理起源。
• 研究局域磁矩的形成及其通过Kondo效应屏蔽如何调控自旋-电荷关联的非微扰行为。
• 建立一个物理直观的框架，利用单玻色子交换分解方法分析微扰理论之外的强关联效应。

提出的方法

• 利用动力学平均场理论（DMFT）对Hubbard原子、Anderson杂质模型以及Bethe晶格上的Hubbard模型，数值计算广义局域电荷磁化率。
• 应用单玻色子交换（SBE）形式化方法，将磁化率分解为可物理解释的散射过程，从而识别主导的微观机制。
• SBE分解可分离自旋与电荷涨落的贡献，实现对Matsubara频率空间中频率分辨矩阵元的分析。
• 将完整相互作用磁化率与自旋-玻色子耦合设为非相互作用极限（λ^sp_ν,ν′−ν = 1）的近似进行比较，以隔离电子-玻色子耦合的作用。
• 利用经过校准的数值数据，在三个温度区域（微扰/高温、中间温度/局域磁矩、低温/Kondo）研究温度依赖行为。
• 研究采用负性判据与频率空间结构分析，识别非微扰行为的起始点。

实验结果

研究问题

• RQ1 广义电荷磁化率矩阵在Matsubara频率空间中对角项被抑制的原因是什么？
• RQ2 在磁化率矩阵中观察到的非对角项增强的微观起源是什么？
• RQ3 局域磁矩的形成及其屏蔽如何影响微扰展开的失效？
• RQ4 Kondo效应在多大程度上削弱了自旋与电荷自由度之间的非微扰纠缠？
• RQ5 单玻色子交换分解如何揭示强关联体系中非微扰关联的物理过程？

主要发现

• 广义电荷磁化率对角项的抑制直接源于电子与寿命更长、有效耦合增强的局域磁矩的散射。
• 非对角矩阵元的微弱且弥散的增强主要归因于多玻色子散射过程，而非单玻色子交换。
• 在局域磁矩区域，有效自旋-费米子耦合较强，导致物理电荷响应函数显著抑制。
• 在Kondo温度附近，低频区域的有效自旋-费米子耦合逐步减弱，导致电荷响应恢复，同时自旋-电荷纠缠被削弱。
• SBE分解表明，将自旋-玻色子耦合近似为1（λ^sp_ν,ν′−ν = 1）主要影响自旋贡献的对角部分，这是局域磁矩区域电荷响应抑制的关键驱动力。
• 磁化率矩阵中负对角元素的出现，与先前研究中局域磁矩区域的“指纹”条件等公认判据定性一致。