空间随机矢量模型的霍尔角
Hall Angle of a Spatially Random Vector Model
AI总结：
本文研究了磁场存在下费米面与玻色子场的矢量型空间随机耦合，计算了相关传播子、自能和极化函数，发现该模型在低温下保持线性电阻率但霍尔角未呈现奇异金属特征，表明随机相互作用可支持线性输运但需补充要素以完整描述奇异金属。
摘要：
奇异金属表现出线性电阻率和反常霍尔输运，但至今仍缺乏同时解释这两种现象的全面理论。近期研究表明，费米面与玻色子场（标量或矢量型）之间类似 SYK 的空间随机耦合可以产生线性-$T$ 电阻率。本文继续研究磁场存在下的矢量耦合。我们计算了费米子和玻色子传播子，以及自能和极化函数，并确定了它们对磁场的依赖关系。尽管霍尔角未表现出奇异金属的特征，但线性温度电阻率在低温下依然存在。结果表明，随机相互作用能够稳健地支持线性输运，尽管可能需要额外要素才能捕捉奇异金属的完整唯象学。
英文摘要：
Strange metals exhibit linear resistivity and anomalous Hall transport, yet a comprehensive theory that accounts for both phenomena is still lacking. Recent studies have shown SYK-like spatially random couplings between a Fermi surface and a bosonic field, either scalar or vector type, can yield linear-$T$ resistivity. In this paper, we continue the investigation on a vector coupling in the presence of a magnetic field. We compute the fermion and boson propagators, along with the self-energy and polarization functions, and determine their dependence on the magnetic field. Although the Hall angle does not exhibit the signature of strange-metal, the linear-in-temperature resistivity remains at low temperatures. Results indicate that random interactions can robustly support linear transport, though additional ingredients may be required to capture the full phenomenology of strange metals.
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