热霍尔效应的规范理论
Gauge Theories for the Thermal Hall Effect
摘要：
本文研究了2+1维空间中费米物质与出射规范场耦合的热霍尔效应。虽然体拓扑相的低温热霍尔电导率可以连接到手征边缘状态和引力异常，但在2+1维量子临界点以上的非零温度下没有这样的解释。在大量物质味的限制下，对霍尔热导率的主要贡献来自费米子物质。其次是来自规范涨落的贡献，它的符号与物质贡献的符号相反。我们说明了这一点的计算上的狄拉克陈-西蒙斯理论的量子相变在一个正方形晶格反铁磁体涉及发病的semion拓扑秩序。我们发现类似的结果与费米口袋耦合到一个紧急U（1）规范场的赝隙金属模型。我们注意到最近对空穴掺杂铜氧化物的观察的联系：我们的理论抓住了主要趋势，但效果的总体幅度小于观察到的。
英文摘要：
We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in 2+1 dimensions. While the low-temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at nonzero temperatures above 2+1 dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that from the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is opposite to that of the matter contribution. We illustrate this by computations on a Dirac Chern-Simons theory of the quantum phase transition in a square-lattice antiferromagnet involving the onset of semion topological order. We find similar results for a model of the pseudogap metal with Fermi pockets coupled to an emergent U(1) gauge field. We note connections to recent observations on the hole-doped cuprates: our theory captures the main trends, but the overall magnitude of the effect is smaller than that observed.
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