反常的礼物：金属中朗道相变的精确结果
Gifts from anomalies: Exact results for Landau phase transitions in metals
摘要：
非费米液体现象在金属系统中朗道有序转变的临界点附近自然出现，在那里玻色子序参量的强烈波动破坏了相干准粒子。尽管在发展受控微扰技术方面取得了进展，但这种金属量子临界点的许多低能物理仍然知之甚少。我们证明，精确的，非perburbative结果可以得到的光学输运和静态的费米面耦合到临界玻色子的“赫兹-米利斯”理论的可解释性。这样的模型拥有一个大的涌现对称性和异常结构，我们利用它来固定这些量。特别是，我们表明，在红外极限，玻色子自能量在零波矢，$\mathbf{q}=0$，是一个常数的频率无关，和光学电导率的实部，$σ(ω)$，是纯粹的δ函数Drude峰没有其他的修正。因此，玻色子自能或光电导率的进一步频率依赖性只能来自干净系统中不相关的算子。得到了费米液体参数从无序相向临界点逼近时的精确关系。没有一个普遍的，幂律频率依赖的玻色子自我能量与以前的微扰计算对比，我们解释了这种差异的起源。
英文摘要：
Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in "Hertz-Millis" theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, $\mathbf{q}=0$, is a constant independent of frequency, and the real part of the optical conductivity, $σ(ω)$, is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.
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