论文标题
荷斯坦模型中的声子重态化和pomeranchuk不稳定性
Phonon renormalization and Pomeranchuk instability in the Holstein model
论文作者
论文摘要
带有无散爱因斯坦语音子的荷斯坦模型是描述凝结物质中电子相互作用的最简单模型之一。在相关无量纲的电子phonon耦合$λ_0$的功能中，扰动理论的幼稚外推表明，在零温度下，该模型表现出pomeranchuk的不稳定性，其特征是以$λ_0$ corder Unity的临界值的差异均匀压缩性。在这项工作中，我们使用现代功能重新归一化组（RG）方法重新检查了此问题。对于尺寸$ d> 3 $，我们发现荷斯坦模型的RG流确实表现出与Pomeranchuk不稳定性相关的三个固定点。这个非高斯固定点是紫外线稳定的，与$ ϕ^3 $的众所周知的紫外线稳定点密切相关，高于六个维度。要以固定密度实现Pomeranchuk的临界点，电子偶联$λ_0$和绝热比率$ω_0 /ε_f$都必须进行细微调整，以实现订单统一的关键值，其中$ω_0$是phonon频率，$ω___________f$是fermi us fermi is fermi is fermi。另一方面，对于尺寸$ d \ leq 3 $，我们发现荷斯坦模型的RG流量没有任何关键的固定点。这排除了与$ d \ leq 3 $中的pomeranchuk不稳定相关的量子关键点。
The Holstein model with dispersionless Einstein phonons is one of the simplest models describing electron-phonon interactions in condensed matter. A naive extrapolation of perturbation theory in powers of the relevant dimensionless electron-phonon coupling $λ_0$ suggests that at zero temperature the model exhibits a Pomeranchuk instability characterized by a divergent uniform compressibility at a critical value of $λ_0$ of order unity. In this work, we re-examine this problem using modern functional renormalization group (RG) methods. For dimensions $d > 3$ we find that the RG flow of the Holstein model indeed exhibits a tricritical fixed point associated with a Pomeranchuk instability. This non-Gaussian fixed point is ultraviolet stable and is closely related to the well-known ultraviolet stable fixed point of $ϕ^3$-theory above six dimensions. To realize the Pomeranchuk critical point in the Holstein model at fixed density both the electron-phonon coupling $λ_0$ and the adiabatic ratio $ω_0 / ε_F$ have to be fine-tuned to assume critical values of order unity, where $ω_0$ is the phonon frequency and $ε_F$ is the Fermi energy. On the other hand, for dimensions $d \leq 3$ we find that the RG flow of the Holstein model does not have any critical fixed points. This rules out a quantum critical point associated with a Pomeranchuk instability in $d \leq 3$.
