Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone

Abstract

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.

6 pages, 4 figures + supplement (7 pages, 9 figures)

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• Topological Anomalous Skin Effect in Weyl Superconductors
• Topological diffusive metal in amorphous transition metal monosilicides
• Nodal vacancy bound states and resonances in three-dimensional Weyl semimetals
• Disorder effects on triple-point fermions
• BCS-like disorder-driven instabilities and ultraviolet effects in nodal-line semimetals
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• Connecting the avoided quantum critical point to the magic-angle transition in three-dimensional Weyl semimetals
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Chiral Anomaly Trapped in Weyl Metals: Nonequilibrium Valley Polarization at Zero Magnetic Field
• Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals
• Electron transport in a weakly disordered Weyl semimetal