低密度极化子金属的声子谱函数

中文摘要 AI 辅助

我们采用密度矩阵重整化群（DMRG），计算了一维无自旋Holstein模型在低且有限载流子浓度（x≤0.15）下的声子谱函数，该函数随电声耦合λ变化。据我们所知，这是该参数区域内的首批此类结果，补充了此前针对单极化子极限（x→0）的大量研究。我们发现，显著的声子谱权重既被转移到裸声子能量Ω以下（直至ω=0），也被转移到Ω以上，这与Migdal极限下预期的Kohn反常现象形成鲜明对比——在Migdal极限中，权重始终集中在Ω附近，且在q=2k_F处存在扭折。我们的结果中未出现该2k_F扭折的特征。这种行为可由随机相位近似（RPA）定性捕捉，而采用“修饰RPA”方案则能半定量描述该行为，且计算开销可忽略不计；该方案中，电子添加传播子通过低密电子-极化子的动量平均（MA）近似进行重整化。相比之下，向该修饰方案添加最低阶顶点修正会产生非物理的负谱权重，这表明当传播子被非微扰修饰后，必须一致地处理顶点和传播子修饰。我们的结果为低密度极化子金属的声子谱函数提供了一种高效近似，该参数区域与弱掺杂绝缘体相关。

英文摘要

We use the density matrix renormalization group (DMRG) to compute the phonon spectral function of a one-dimensional spinless Holstein model doped with a low but finite carrier concentration, $x \leq 0.15$, as a function of the electron-phonon coupling $λ$. To the best of our knowledge, these are the first such results in this regime, complementing extensive prior work at the single-polaron level ($x\to 0$). We find that significant phonon spectral weight is transferred both below, all the way down to $ω=0$, and above the bare phonon energy $Ω$, in stark contrast with the Kohn-anomaly phenomenology expected in the Migdal limit, where weight remains centered near $Ω$ with a kink at $q=2k_F$. No signature of this $2k_F$ kink appears in our results. This behavior is captured qualitatively by the Random Phase Approximation (RPA), and semi-quantitatively, at negligible extra computational cost, by a ``dressed RPA'' scheme in which the electron addition propagator is renormalized using the Momentum Average (MA) approximation for the low-density electron-polaron. By contrast, adding the lowest-order vertex correction to this dressed scheme produces unphysical negative spectral weight, signaling that vertex and propagator dressings must be treated consistently once the propagators are dressed nonperturbatively. Our results provide an efficient approximation for the phonon spectral functions of low-density polaron metals, a regime relevant to weakly doped insulators.

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10 pages, 3 figures