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

Author(s): Wilson, Justin H; Huse, David A; Das Sarma, S; Pixley, JH

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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 nonzero 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 107 states, substantially larger than anything achieved before.
Publication Date: 1-Sep-2020
Electronic Publication Date: 8-Sep-2020
Citation: Wilson, Justin H, Huse, David A, Das Sarma, S, Pixley, JH. (2020). Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone. PHYSICAL REVIEW B, 102 (10.1103/PhysRevB.102.100201
DOI: doi:10.1103/PhysRevB.102.100201
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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