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arXiv 1906.05293cond-mat.str-el
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单带哈伯德模型中的Mott量子临界性:动力学平均场论、幂律谱和标度

Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling

Heike Eisenlohr, Seung-Sup B. Lee, Matthias Vojta

摘要:

最近的研究电传输,理论和实验,附近的带宽调谐莫特金属-绝缘体转变已经发现了明显的量子临界缩放的电阻率在升高的温度下,尽管实际的低温相变是一阶的。这就提出了一个问题,是否存在一个隐藏的莫特量子临界点。在这里,我们证明了哈伯德模型的动力学平均场论在低温极限下存在渐近标度不变(即幂律)解,对应于金属-绝缘体共存区边界处的亚稳绝缘体,这与赝能隙Anderson模型的物理相联系。虽然我们的国家的最先进的数值重整化群计算表明,这种渐近制度仅限于非常小的能量和温度,因此难以获得数值,我们发现存在一个广泛的交叉制度,其中单粒子光谱显示\emph{different}幂律。我们表明,这是幂律制度,对应于近似的局部量子临界性,这是连续连接到并负责以上的经典临界端点的表观量子临界缩放。我们将我们的研究结果可调莫特材料的实验。

英文摘要:

Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastable insulator at the boundary of metal-insulator coexistence region, which can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures and hence difficult to access numerically, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a \emph{different} power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. We connect our findings to experiments on tunable Mott materials.

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