Quantum critical behavior in itinerant electron systems: Eliashberg theory and instability of a ferromagnetic quantum critical point
Quantum critical behavior in itinerant electron systems: Eliashberg theory and instability of a ferromagnetic quantum critical point
复制标题
DOI：
10.1103/physrevb.74.195126
复制
发表时间：
2006-05
影响因子：
3.7
通讯作者：
J. Rech;C. Pépin;A. Chubukov
中科院分区：
文献类型：
--
作者：
J. Rech;C. Pépin;A. Chubukov
我们考虑费米子与无间隙长波长集体玻色子模式相互作用的问题。该理论描述了铁磁量子临界点（QCP）和向列有序的 QCP 等情况。我们分两步构建了 QCP 处的可控展开：首先创建非费米液体“零级”Eliashberg 型理论，然后证明剩余相互作用效应很小。我们证明这种方法在两个条件下是合理的：相互作用应小于费米子带宽，并且带质量 ${m}_{B}$ 应远小于 $m={k}_{F}∕{v}_{F}$，或者费米子风味的数量 $N$ 应很大。对于 SU(2) 对称铁磁 QCP，我们发现 Eliashberg 理论本身包含一组奇异重整化，可以将其理解为由朗道阻尼项生成的准粒子之间有效的远程动态相互作用的结果。这些奇异重正化会对静态自旋磁化率产生负的非解析 ${q}^{3∕2}$ 校正，并破坏铁磁 QCP。我们证明这种效应可以在 ${\ensuremath{\phi}}^{4}$ 量子临界性理论的框架中理解。我们还表明，玻色子传播器的非解析 ${q}^{3∕2}$ 校正特定于 SU(2) 对称情况。对于具有标量阶次参数的系统，各个图的 ${q}^{3∕2}$ 贡献在磁化率的完整表达式中抵消，并且 QCP 保持稳定。
We consider the problem of fermions interacting with gapless long-wavelength collective bosonic modes. The theory describes, among other cases, a ferromagnetic quantum-critical point (QCP) and a QCP towards nematic ordering. We construct a controllable expansion at the QCP in two steps: we first create a non-Fermi-liquid ``zero-order'' Eliashberg-type theory, and then demonstrate that the residual interaction effects are small. We prove that this approach is justified under two conditions: the interaction should be smaller than the fermionic bandwidth, and either the band mass ${m}_{B}$ should be much smaller than $m={k}_{F}∕{v}_{F}$, or the number of fermionic flavors $N$ should be large. For an SU(2) symmetric ferromagnetic QCP, we find that the Eliashberg theory itself includes a set of singular renormalizations which can be understood as a consequence of an effective long-range dynamic interaction between quasiparticles, generated by the Landau damping term. These singular renormalizations give rise to a negative nonanalytic ${q}^{3∕2}$ correction to the static spin susceptibility, and destroy a ferromagnetic QCP. We demonstrate that this effect can be understood in the framework of the ${\ensuremath{\phi}}^{4}$ theory of quantum criticality. We also show that the nonanalytic ${q}^{3∕2}$ correction to the bosonic propagator is specific to the SU(2) symmetric case. For systems with a scalar order parameter, the ${q}^{3∕2}$ contributions from individual diagrams cancel out in the full expression of the susceptibility, and the QCP remains stable.