Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport co-efficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport co-efficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.
Signatures of quantum criticality in hole-doped and chemically pressurized EuFe_2As_2 single crystals
通过测量热电势$S(T)$和电阻率$ρ(T)$，研究了$_x$ Eu $_{1-x}$ Fe $_2$ As $_2$和EuFe $_2$（As $_{1-y}$ P $_y$）$_2$单晶中空穴掺杂和化学压力（等价掺杂）的效应.掺杂后$S(T)$的演变表明，在临界值$x_{\mathrm{cr}}=0.3$和$y_{\mathrm{cr}}=0.21$，分别电子配置的急剧变化，自旋密度波跃迁被完全抑制和超导性（SC）出现。对于化学压力的情况下，与已发表的ARPES测量结果的比较表明，在$y_{cr}$的Lifshitz转变。温度依赖性$S(T)/T\propto \log T$和$Δρ\propto T$观察到的正常状态以上的SC过渡建议在这两个系统中的量子临界。
Scrutinizing Hall effect in Mn$_{1-x}$Fe$_{x}$Si: Fermi surface evolution and hidden quantum criticality
区分Mn $_{1-x}$ Fe $_{x}$ Si顺磁相中的正常（OHE）和异常（AHE）霍尔效应揭示了与隐藏的量子临界（QC）点$x^*\sim0.11$相关的OHE符号反转。在中等Fe含量下的半金属行为导致Mn $_{1-x}$ Fe $_{x}$ Si中的费米学、磁相互作用和QC领域中的可验证的预测。电子和空穴浓度的变化被认为是通过修改海森堡磁性模型中的RKKY交换相互作用来调节Mn $_{1-x}$ Fe $_{x}$ Si中QC区域的驱动力。
