We determine the shear viscosity and the dc electrical conductivity of interacting three-dimensional Luttinger semimetals, which have a quadratic band touching point in the energy spectrum, in the hydrodynamic regime. It is well known that when the chemical potential is right at the band touching point, the long-range Coulomb interaction induces the Luttinger-Abrikosov-Beneslavskii (LAB) phase at $T=0$, which is an interacting, scale-invariant, non-Fermi-liquid state of electrons. Upon combining the renormalization-group (RG) analysis near the upper critical spatial dimension of 4 with the Boltzmann kinetic equation, we determine the universal ratio of viscosity over entropy and the electrical dc conductivity of the system at the interacting LAB fixed point of the RG flow. The projection of the Coulomb interaction on the eigenstates of the system is found to play an important quantitative role for the scattering amplitude in the collision integral, and the so-called Auger processes make a large numerical contribution to the inverse scattering time in the transport quantities. The obtained leading-order result suggests that the universal ratio of the viscosity over entropy, when extrapolated to the physical three spatial dimensions, is above, but could be rather close to, the Kovtun-Son-Starinets lower bound.

中文翻译：

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Luttinger-Abrikosov-Beneslavskii非费米液体中的流体动力传输

我们确定了在流体力学状态下相互作用的三维Luttinger半金属的剪切粘度和直流电导率，它们在能谱中具有二次谱带接触点。众所周知，当化学势恰好位于谱带接触点时，长距离库仑相互作用会在以下位置诱发Luttinger-Abrikosov-Beneslavskii（LAB）相$Ť=0$，它是相互作用的，尺度不变的，非费米液体的电子态。通过将接近4的上临界空间维数的重归一化组（RG）分析与Boltzmann动力学方程相结合，我们确定了在RG的相互作用LAB固定点处，粘度对熵的通用比和系统的直流电导率流。发现库仑相互作用在系统本征态上的投影对于碰撞积分中的散射幅度起着重要的定量作用，所谓的俄歇过程对输运量中的逆散射时间起着很大的数值作用。获得的前导结果表明，当将粘度对熵的通用比值外推到物理的三个空间维度时，其在上方，