We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At $T=0$, bosonic and fermionic self-energies are traditionally computed within Eliashberg theory, and they obey scaling relations with characteristic power laws. Corrections to Eliashberg theory break these power laws but only at very small frequencies. Quantum Monte Carlo (QMC) simulations have shown that, already at much larger frequencies, there are strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite $T$ and argue that in the $T$ range accessible in the QMC simulations above the superconducting transition, the scaling forms for both fermionic and bosonic self-energies are quite different from those at $T=0$. We compare finite $T$ results with QMC data and find good agreement for both systems. We argue that this agreement resolves the key apparent contradiction between the theory and the QMC simulations.

中文翻译：

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有限温度下量子临界金属的常态性质

我们研究了有限温度对接近反铁磁或Ising向列态的量子临界点的金属的正常态性能的影响。在$Ť=0$，传统上在Eliashberg理论中计算出玻色子和费米子的自能，它们遵循与特征幂定律的比例关系。对Eliashberg理论的更正打破了这些幂定律，但仅在很小的频率下发生。量子蒙特卡洛（QMC）模拟表明，在更大的频率下，与这些预测存在强烈的系统偏差，这对理论分析的有效性产生了怀疑。我们将Eliashberg理论扩展到有限$Ť$ 并认为在 $Ť$ 在超导跃迁以上的QMC模拟中可达到的范围内，铁离子和玻色子自能的定标形式与 $Ť=0$。我们比较有限$Ť$通过QMC数据得出结果，并找到了两个系统的良好协议。我们认为，该协议解决了该理论与QMC仿真之间的关键明显矛盾。