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首页> 外文期刊>Physical review >Quasiparticle interaction function in a two-dimensional Fermi liquid near an antiferromagnetic critical point
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Quasiparticle interaction function in a two-dimensional Fermi liquid near an antiferromagnetic critical point

机译：反铁磁临界点附近二维费米液体中的拟粒子相互作用函数

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摘要

We present the expression for the quasiparticle vertex function Γ~ω(K_F,P_F) (proportional to the Landau interaction function) in a 2D Fermi liquid (FL) near an instability towards antiferromagnetism. This function is relevant in many ways in the context of metallic quantum criticality. Previous studies have found that near a quantum critical point, the system enters into a regime in which the fermionic self-energy is large near hot spots on the Fermi surface [points on the Fermi surface connected by the antiferromagnetic ordering vector q_π = (π,π)] and has much stronger dependence on frequency than on momentum. We show that in this regime, which we termed a critical FL, the conventional random-phase-approximation- (RPA) type approach breaks down, and to properly calculate the vertex function one has to sum up an infinite series of terms which were explicitly excluded in the conventional treatment. Besides, we show that, to properly describe the spin component of Γ~ω(K_F,P_F) even in an ordinary FL, one has to add Aslamazov-Larkin (AL) terms to the RPA vertex. We show that the total Γ~ω(K_F,P_F)is larger in a critical FL than in an ordinary FL, roughly by an extra power of magnetic correlation length (ζ), which diverges at the quantum critical point. However, the enhancement of Γ~ω(K_F,P_F) is highly nonuniform: It holds only when, for one of the two momentum variables, the distance from a hot spot along the Fermi surface is much larger than for the other one. This fact renders our case different from quantum criticality at small momentum, where the enhancement of Γ~ω(K_F,P_F) was found to be homogeneous. We show that the charge and spin components of the total vertex function satisfy the universal relations following from the Ward identities related to the conservation of the particle number and the total spin. We show that in a critical FL, the Ward identity involves Γ~ω(K_F,P_F) taken between particles on the FS. We find that the charge and spin components of Γ~ω(K_F,P_F) are identical to leading order in the magnetic correlation length. We use our results for Γ~ω(K_F,P_F) and for the quasiparticle residue to derive the Landau parameters F_c~(l=0) = F_s~(l=0), the density of states, and the uniform (q = 0) charge and spin susceptibilities X_c~(l=0) = X_s~(l=0). We show that the density of states N_F diverges as log(ζ); however, F_(c,s)~(l=0) also diverge as log(ζ), such that the total X_(c,s)~(l=0) ∝ N_F/(1+ F_c~(l=0)) remain finite at (ζ) = ∞. We show that at weak coupling these susceptibilities are parametrically smaller than for free fermions.
机译：我们提出了在反铁磁不稳定性附近的二维费米液体（FL）中准粒子顶点函数Γ〜ω（K_F，P_F）（与Landau相互作用函数成比例）的表达式。在金属量子临界情况下，该功能在许多方面都具有重要意义。先前的研究发现，在量子临界点附近，系统进入一种机制，其中费米表面上的热点附近[费米表面上由反铁磁有序向量q_π=（π， π）]，并且对频率的依赖性比对动量的依赖性要强得多。我们证明，在这种称为临界FL的机制中，常规的随机相位近似（RPA）类型方法崩溃了，要正确计算顶点函数，必须总结出一系列无穷的项，常规治疗除外。此外，我们表明，即使在普通FL中也要正确描述Γ〜ω（K_F，P_F）的自旋分量，必须向RPA顶点添加Aslamazov-Larkin（AL）项。我们显示，临界FL中的总Γ〜ω（K_F，P_F）比普通FL中的大，大约是磁相关长度（ζ）的一个额外幂，它在量子临界点处发散。但是，Γ〜ω（K_F，P_F）的增强是非常不均匀的：仅当对于两个动量变量之一，沿着费米表面到热点的距离远大于另一个时，才成立。这一事实使我们的情况不同于小动量下的量子临界，在量子小临界下，Γ〜ω（K_F，P_F）的增强是均匀的。我们表明，总顶点函数的电荷和自旋分量满足与涉及粒子数守恒和总自旋的沃德恒等式所遵循的普遍关系。我们表明，在临界FL中，Ward身份涉及FS上粒子之间的Γ〜ω（K_F，P_F）。我们发现Γ〜ω（K_F，P_F）的电荷和自旋分量与磁相关长度中的前导顺序相同。我们将结果用于Γ〜ω（K_F，P_F）和准粒子残差来得出Landau参数F_c〜（l = 0）= F_s〜（l = 0），状态密度和均匀性（q = 0）电荷和自旋磁化率X_c〜（l = 0）= X_s〜（l = 0）。我们表明，状态密度N_F随log（ζ）的变化而变化；然而，F_（c，s）〜（l = 0）也随着log（ζ）分开，使得总X_（c，s）〜（l = 0）∝ N_F /（1+ F_c〜（l = 0） ））在（ζ）=∞处保持有限。我们表明，在弱耦合下，这些磁化率比自由费米子小。

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