Dispersive Sachdev-Ye-Kitaev model: Band structure and quantum chaos
Dispersive Sachdev-Ye-Kitaev model: Band structure and quantum chaos
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DOI：
10.1103/physrevb.96.205138
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发表时间：
2017-07
影响因子：
3.7
通讯作者：
Pengfei Zhang
中科院分区：
文献类型：
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作者：
Pengfei Zhang
Sachdev-Ye-Kitaev(SYK)模型是非费米液体的一个具体模型，在$0+1$-$d$中具有最大的混沌行为。为了深入了解费米子可以在不同位置之间跳跃的高维真实材料，这里我们考虑通过恒定跳跃来耦合SYK晶格。我们称之为色散SYK模型。聚焦于$1+1$-$d$均匀跃迁，通过调节温度或随机相互作用(跃迁)和常数跃迁的相对强度，我们发现了从色散金属到非共格金属的交叉，其中动态指数$z$从$1$变化到$\Infty$。我们通过计算谱函数、电荷密度相关器和Lyapunov指数来研究这种交叉现象。我们进一步发现，当化学势被调节到接近Van Hove奇点时，由于费米面附近的态密度较大，Lyapunov指数变得更大。还讨论了拓扑非平凡带的影响。
The Sachdev-Ye-Kitaev (SYK) model is a concrete model for non-Fermi Liquid with maximally chaotic behavior in $0+1$-$d$. In order to gain some insights into real materials in higher dimensions where fermions could hop between different sites, here we consider coupling a SYK lattice by a constant hopping. We call this dispersive SYK model. Focusing on $1+1$-$d$ homogeneous hopping, by either tuning temperature or the relative strength of random interaction (hopping) and constant hopping, we find a crossover between a dispersive metal to an incoherent metal, where dynamic exponent $z$ changes from $1$ to $\infty$. We study the crossover by calculating spectral function, charge density correlator and the Lyapunov exponent. We further find the Lyapunov exponent becomes larger when the chemical potential is tuned to approach a Van Hove singularity because of the large density of states near the Fermi suface. The effect of the topological non-trivial bands is also discussed.