通过规范/重力对偶性模拟无序固体中的光学电导率
Mimic the optical conductivity in disordered solids via gauge/gravity duality
摘要：
本文利用Einstein-Maxwell-Einstein理论研究了（2+1）维非相对论场论与（3+1）维带电Lifshitz黑膜全息对偶的光学电导率。令人惊讶的是，我们发现，光学交流电导率满足非平凡的（非）幂律标度在高频制度，而不是接近一个常数时，动力学临界指数$z>1$，这是定性相似的各种无序固体凝聚态系统。此外，这种（非）幂律标度行为具有一定的普适性，对温度具有鲁棒性。我们认为，AC电导率的特殊标度行为可能源于量子场与规范场的耦合以及Lifshitz时空中边界附近的对数行为。
英文摘要：
We study the optical conductivity in a (2+1)-dimensional non-relativistic field theory holographically dual to a (3+1)-dimensional charged Lifshitz black brane with the Einstein-Maxwell-dilaton theory. Surprisingly, we find that the optical AC conductivity satisfies the nontrivial (non-)power law scaling in the high frequency regime rather than approaching to a constant when the dynamical critical exponent $z>1$, which is qualitatively similar to those in various disordered solids in condensed matter systems. Besides, this (non-)power law scaling behavior shows some universality, which is robust against the temperatures. We argue that the peculiar scaling behavior of AC conductivity may stem from the couplings of the dilaton field with the gauge fields and also the logarithmic behavior near the boundary in the Lifshitz spacetime.
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