发表机构
Lehigh University（利哈伊大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过数值和场论方法确定脏外尔半金属-金属量子相变的下临界维度为2、上临界维度为4，并揭示其关联长度指数与动力学标度指数的普适行为。
AI 中文摘要
具有标志性线性能量-动量关系和外尔或狄拉克费米子，在d维空间中能量E处的平均态密度(ADOS)为$\rho(E) \sim |E|^{d-1}$，构成了研究无序驱动的半金属-金属量子相变(QPT)的独特平台，该相变发生在弹道(弱无序下实现)和扩散(较强无序下稳定)准粒子之间。这种QPT仅在$d>2$时发生，且超出安德森金属-绝缘体转变的范畴。通过使用核多项式方法在$d=2$至$6$的脏外尔系统中数值计算ADOS，我们在此表明$d=2$和$d=4$分别是这种非常规QPT的下临界维度($d_\ell$)和上临界维度($d_u$)，这与自洽玻恩近似中准粒子寿命的解所建议的一致。因此，对于$d \geq 4$，关联长度指数在数值精度内被发现为$\nu \approx 0.5$。然而，在量子临界点，动力学标度指数对于任何$d \geq 3$被数值上钉扎在$z \approx d/2$附近，这被证明是场论重整化群计算的精确结果。因此，外尔半金属-金属QPT可以在$d_\ell$和$d_u$附近进行场论研究。
英文摘要
Weyl or Dirac fermions with the iconic linear energy-momentum relation and average density of states (ADOS) $ρ(E) \sim |E|^{d-1}$ at energy $E$ in $d$ spatial dimensions, constitute a unique setup to study the disorder-driven semimetal-to-metal quantum phase transition (QPT) between ballistic (realized for weak disorder) and diffusive (stabilized at stronger disorder) quasiparticles. Such a QPT takes place only for $d>2$ and falls beyond the realm of the Anderson metal-to-insulator transition. From numerically computed ADOS (using the kernel polynomial method) in dirty Weyl systems in $d=2$ to $6$, here we show that $d=2$ and $d=4$ are the lower ($d_\ell$) and upper ($d_u$) critical dimensions for such an unconventional QPT, respectively, as suggested from the solution of quasiparticle lifetime within the self-consistent Born approximation. Consequently, for $d \geq 4$ the associated correlation length exponent is found to be $ν\approx 0.5$ (within numerical accuracy). However, the dynamic scaling exponent at the quantum critical point is pinned close to $z \approx d/2$ (numerically) for any $d \geq 3$, which is shown to be an exact result from a field-theoretic renormalization group calculation. Therefore, Weyl semimetal-to-metal QPTs can be studied field theoretically around both $d_\ell$ and $d_u$.
Comments8 Pages and 3 Figures (Supplemental Material as Ancillary file)
