论文标题
在单个无序Weyl锥的精确数值模拟中避免了量子临界点
Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone
论文作者
论文摘要
现有的理论作品在三维迪拉克和Weyl半学是否稳定在与短距离相关的随机电位上有所不同。数值证据表明，半学是不稳定的，而某些现场理论的intanton计算发现它是稳定的。差异超出了方法：连续性场理论作品使用单个完美的线性Weyl锥，而数值作品则使用固有具有带曲率和多个Weyl锥的紧密结合晶格模型。在这项工作中，我们通过对分析处理中使用的相同模型进行精确的数字来弥合这一差距，并且我们发现，与晶格模型中发现的韦尔节点能量附近的稀有区域相关的所有现象在连续理论中持续存在：状态的密度是非零的，并且表现出避免过渡。除了表征这种过渡外，我们还发现了稀有状态并表明它们具有预期的行为。这些模拟利用具有正式密度矩阵的稀疏基质技术；这样做可以使我们能够达到希尔伯特的空间尺寸，高于$ 10^7 $的州，比以前所取得的成就要大得多。
Existing theoretical works differ on whether three-dimensional Dirac and Weyl semimetals are stable to a short-range-correlated random potential. Numerical evidence suggests the semimetal to be unstable, while some field-theoretic instanton calculations have found it to be stable. The differences go beyond method: the continuum field-theoretic works use a single, perfectly linear Weyl cone, while numerical works use tight-binding lattice models which inherently have band curvature and multiple Weyl cones. In this work, we bridge this gap by performing exact numerics on the same model used in analytic treatments, and we find that all phenomena associated with rare regions near the Weyl node energy found in lattice models persist in the continuum theory: The density of states is non-zero and exhibits an avoided transition. In addition to characterizing this transition, we find rare states and show that they have the expected behavior. The simulations utilize sparse matrix techniques with formally dense matrices; doing so allows us to reach Hilbert space sizes upwards of $10^7$ states, substantially larger than anything achieved before.
